Question

115. What is the difference between the sum of first 'n' odd natural numbers and that of first
'n' natural numbers?​

Answer 1

Answer:

First 'n' odd natural numbers are

1,3,5,7,........n

First 'n' natural numbers are

1,2,3,4,5,..........n

Step-by-step explanation:

1. nth term of odd natural numbers
2. 1+(n-1)*2
3. 1+2n-2
4. 2n-1
5. Sum is
6. (2n-1)(2n-1+1)/2
7. 2n(2n-1)/2
8. nth term of natural numbers
9. 1+(n-1)*1
10. n
11. sum is
12. n(n+1)/2

Difference is

2n(n-1)/2-n(n+1)/2

=1/2{n^2-n-n^2-n}

=1/2(-2n)

=-n