Questions on Number System

1. Find the sum of even natural numbers 1 to 100.
Ans- There are 50 even numbers between 1 and 100. Now, according to formulae, n(n+1) = 50x51= 2550.
Similarly, you can find the sum of odd natural numbers between 1 and 100. 

2. Find the sum of even numbers from 41 to 100.
Ans- firstly you should find the sum of even numbers from 1 to 100 = 2550
Then, find the sum of even natural’s number from 1 to 40= 20x21= 420
Now, the sum of even numbers from 41 to 100= 2550-420= 2130

3. Find the sum of the square of natural numbers 1 to 20.
Ans- according to question, find 12+22+32…. 202 = n(n+1)(2n+1)/6
Now put n=20,
                = 20(21)(41)/6 = 2870
4. Find the sum of the square of natural numbers from 11 to 20.
Ans- according to question, find 112+122+132….. 202 = sum of the square from 1 to 20 – sum of the square from 1 to 10.
Now, the sum of the square from 1 to 20 =2870
And, the sum of the square from 1 to 10 = 385
Hence, the sum of square from 11 to 20 = 2870-385= 2485.
5. Find the sum of the square of natural numbers – 42 + 62 + 82 + 102 + 122 + 142 + 162 + 182 + 202.
Ans- In these types of question, you can see 22 is common so take out the 22 and then add the remaining values.
Therefore, 22 (22 + 32 + 42 + 52 + 62 + 72 + 82 + 92 + 102) = 4x384 = 1536.
6. Find the sum of digits from 1 to 100.
Ans- In these questions, one has to count each and every digit occurring from 1 to 100.
Now, from 1 to 100= ‘0’ occurs 11 times; ‘1’ occurs 21 times; and ‘2-9’ occurs 20 times each.
Hence, the sum of digits from 1 to 100 = (11x0) + (21x1) + (44x20) = 901.