Number system
1. natural number : 1,2,3,4,5......... infinity.

2. whole numbers : 0,1,2,3,4,5,
.... infinity.

3. intergers : -infinity..........-3,-2,-1,0,1,2,3,...... infinity.

4.even number : the number which are divisible by 2 are called even number. ex: 0,2,4,6,8,10... infinity.

5.odd number : the number which are not divisible by 2 are called odd number. ex: 1,3,5,7,9,11,13,15...... infinity.

6. prime number : the number which have exactly two factors that means one factor and itself are called prime number ex: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97..... infinity. 1 to 100 number between 25 prime numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

8. compiste number : more than two factors are called compiste numbers
ex: The composite numbers 1 to 100 are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21, 20, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 56, 55, 57, 58, 60, 63, 62, 64, 65, 66, 69,68, 70, 72, 75, 74, 76, 78, 77, 80, Except for these, all other numbers are prime numbers.

9. non compiste numbers:
{0, 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, ...}

note :
1 + prime numbers = non composite numbers
1 + composite numbers = non prime numbers

11. real numbers
a) rational numbers : exact value
ex: 1, 2, 5/2, √9, 4/2...
b) irrational numbers: approximately value
ex: √2, 0.565656565655....
40/6,......

types of series in number system's
1. difference series :if increase or decrease of number 💡normal💡 than that series is called difference series
ex :
1. 5,8,11,14,17, __(?) 20
(5+3=8
8+3 = 11
11 + 3= 14
14 + 3 = 17
17+3=20)

2. 85,83,79,73,65, __(?) 55
85-2 = 83
83 -4 = 79
79-6 = 73
73 -8 = 65
65-10 = 55)
3. 6,8,7,11,8,14,9 __(?)17
1)
6+1 = 7
7 +1 = 8
8 + 1 = 9
2)
8+3 = 11
11 +3 = 14
14+3 = 17

2. product series :if increase or decrease of number 💡abnormal💡 than that series is called product series
ex:
1. 1,2,6,24,120,_(?)720
2. 15625,3125,625,125,_(?)25
3. 2,4,12,60,420,4620,_(?)60060

3. combinational series : combination of two or more types of series are called combinational series
ex:
1.1,4,11,34,101,_(?)101(logic *3-1 next *3 -1)
2. 36,6,42,7,78,13,150,_(?)25(logic divides by 6)

4.square series : in this type OS series the numbers are perfect square or cubes or neare to perfect square or nearer to perfect cube then that type of series are called perfect square series
ex:
1. 784,676,576,484,_(?)400
2. 64,216,512,729,_(?)1000
3. 2,5,10,17,26 _(?)37
4. 0,62,213,508(?)724
https://youtu.be/vNAUPzNFNc4?si=DBoYS8Wf5J4jn4cE

Here are the squares of numbers from 1 to 100:

1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
11^2 = 121
12^2 = 144
13^2 = 169
14^2 = 196
15^2 = 225
16^2 = 256
17^2 = 289
18^2 = 324
19^2 = 361
20^2 = 400
21^2 = 441
22^2 = 484
23^2 = 529
24^2 = 576
25^2 = 625
26^2 = 676
27^2 = 729
28^2 = 784
29^2 = 841
30^2 = 900
31^2 = 961
32^2 = 1024
33^2 = 1089
34^2 = 1156
35^2 = 1225
36^2 = 1296
37^2 = 1369
38^2 = 1444
39^2 = 1521
40^2 = 1600
41^2 = 1681
42^2 = 1764
43^2 = 1849
44^2 = 1936
45^2 = 2025
46^2 = 2116
47^2 = 2209
48^2 = 2304
49^2 = 2401
50^2 = 2500
51^2 = 2601
52^2 = 2704
53^2 = 2809
54^2 = 2916
55^2 = 3025
56^2 = 3136
57^2 = 3249
58^2 = 3364
59^2 = 3481
60^2 = 3600
61^2 = 3721
62^2 = 3844
63^2 = 3969
64^2 = 4096
65^2 = 4225
66^2 = 4356
67^2 = 4489
68^2 = 4624
69^2 = 4761
70^2 = 4900
71^2 = 5041
72^2 = 5184
73^2 = 5329
74^2 = 5476
75^2 = 5625
76^2 = 5776
77^2 = 5929
78^2 = 6084
79^2 = 6241
80^2 = 6400
81^2 = 6561
82^2 = 6724
83^2 = 6889
84^2 = 7056
85^2 = 7225
86^2 = 7396
87^2 = 7569
88^2 = 7744
89^2 = 7921
90^2 = 8100
91^2 = 8281
92^2 = 8464
93^2 = 8649
94^2 = 8836
95^2 = 9025
96^2 = 9216
97^2 = 9409
98^2 = 9604
99^2 = 9801
100^2 = 10000

Here are the cubes of numbers from 1 to 100:

1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
7^3 = 343
8^3 = 512
9^3 = 729
10^3 = 1000
11^3 = 1331
12^3 = 1728
13^3 = 2197
14^3 = 2744
15^3 = 3375
16^3 = 4096
17^3 = 4913
18^3 = 5832
19^3 = 6859
20^3 = 8000
21^3 = 9261
22^3 = 10648
23^3 = 12167
24^3 = 13824
25^3 = 15625
26^3 = 17576
27^3 = 19683
28^3 = 21952
29^3 = 24389
30^3 = 27000
31^3 = 29791
32^3 = 32768
33^3 = 35937
34^3 = 39304
35^3 = 42875
36^3 = 46656
37^3 = 50653
38^3 = 54872
39^3 = 59319
40^3 = 64000
41^3 = 68921
42^3 = 74088
43^3 = 79507
44^3 = 85184
45^3 = 91125
46^3 = 97336
47^3 = 103823
48^3 = 110592
49^3 = 117649
50^3 = 125000
51^3 = 132651
52^3 = 140608
53^3 = 148877
54^3 = 157464
55^3 = 166375
56^3 = 175616
57^3 = 185193
58^3 = 195112
59^3 = 205379
60^3 = 216000
61^3 = 226981
62^3 = 238328
63^3 = 250047
64^3 = 262144
65^3 = 274625
66^3 = 287496
67^3 = 300763
68^3 = 314432
69^3 = 328509
70^3 = 343000
71^3 = 357911
72^3 = 373248
73^3 = 389017
74^3 = 405224
75^3 = 421875
76^3 = 438976
77^3 = 456533
78^3 = 474552
79^3 = 493039
80^3 = 512000
81^3 = 531441
82^3 = 551368
83^3 = 571787
84^3 = 592704
85^3 = 614125
86^3 = 636056
87^3 = 658503
88^3 = 681472
89^3 = 704969
90^3 = 729000
91^3 = 753571
92^3 = 778688
93^3 = 804357
94^3 = 830584
95^3 = 857375
96^3 = 884736
97^3 = 912673
98^3 = 941192
99^3 = 970299
100^3 = 1000000

5. triangular series : sometimes the differences between the consecutive numbers of the again form a new series and so on. the pattern is continuous, till attain a uniform difference between consecutive number of series.
ex:
1. 3,10,29,66,127_(?)218
2. 3,12,36,80,150,_(?)252

6. arthematic series: a,a+d,a+2d,a+3d,....ntg term
a first term
d common difference
nth term = a + (n-1)d
no. of terms in the given series
n = (nth term - a)/d + 1
ex :
1. find the ntg term in the given series 3,6,9,12,....10 terms
sol)
a = 3
d = 3
nth term = 10
formula
nth term = a + (n-1)d
3 + (10-1)3
3+9(3)
3+27
30
2. how many numbers in the given series
2,6,10,....50
sol)
n = (nth term - a)/d +1
n = (50-2)/4 + 1
n = 48/4 +1
n = 12 + 1
n = 13

7. geometric series:
a,ar,ar²,...ar^n-1

nth term = ar^n-1

ex:
1. find the nth term in given series
2,4,8,16.....10th term
sol)
a = 2
r = 2
n = 1
nth term = ar^n-1
2.2^10-1
2.2^9
2^10
1024
2. number term in the series 4,8,16,..512
a = 4
r = 2
n = 10
nth term = ar^n-1
512 = 4.2^n-1
2^9 = 2^2.2^n-1
9 = 2+n-1
9 = n+1
n = 8
https://youtu.be/NQb4wYPq29A?si=CKcNb-bRQ4LuKFsF

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➡️Reliance & TATA Partners With Nvidia to Develop AI Language Models.

➡️Google Chrome desktop version to get new look, features this month.

Excel by using AI
1. flash fill --> ctrl + E
2.
https://youtu.be/MR823UY615s?si=VZsGZiGXxHjB00_Z

#explanation :
Choose a career that you are passionate about, is based on your strengths and has value for others because that will enable you to devote your time , do better than others and realize the value you are seeking from others once you start providing them the value they need.

#login_form.html
<html>

<head>
<style>
.outer {
margin: auto;
height: 300px;
width: 400px;
border: 2px solid black;
position: relative
}

p {
margin-left: 80px;
}

.in {
margin-left: 80px;
padding: 10px
}

#bt {
width: fit-content;
font-size: 15px;
margin-top: 20px;
position: absolute;
left: 150px;
}

#bt:hover {
background: green;
font-size: 13px;
cursor: pointer;
color: white;
}
</style>
<script>
function fa() {
if (a.value == "" || b.value == "") {
f();
document.getElementById("a").style.border = "3px solid red";
document.getElementById("b").style.border = "3px solid red";
bt.value = "Fill Data First 😏";
} else {
document.getElementById("a").style.border = "3px solid green";
document.getElementById("b").style.border = "3px solid green";
bt.value = "Good now 😁";
bt.style.left = "120px";
}
}
flag = 1;
function f() {
if (flag == 1) {
bt.style.left = "210px";
flag = 2;
} else if (flag == 2) {
bt.style.left = "80px";
flag = 1;
}
}
</script>
</head>

<body>
<div class="outer">
<h1 style="text-align: center">Legend form</h1>
<p>Enter Id</p>
<input class="in" type="text" placeholder="Enter id" id="a" />
<p>Enter Confirm Pass</p>
<input class="in" type="password" placeholder="Enter password" id="b" />
<br />
<input type="submit" onmouseenter="fa()" onclick="alert('Well done👍')" id="bt" />
</div>
</body>

</html>

Explanation
Setting career objectives is the first step because you can then use these objectives to generate and choose the right careers which best meets these objectives.

If you don't set the objectives first, your option generation will not be focused and you may choose the careers that don't meet these objectives