Question

The ratio of the sum of first n even numbers to that of n odd numbers will be

Answer 1

Answer:

Sum of first n even=n(2+2n)/2=n(n+1)

Sum of first n odd =n(2+(n-1)2)/2=n^2

Ratio=(n+1):n

Answer 2

The ratio would be n+1/n

1) The first n even natural numbers are 2,4,6,8,10.....2n

or 2(1,2,3,4,5........n)

2) The sum of n natural numbers is n(n+1)/2

Hence the sum of first n even natural numbers would be n(n+1)

3) The first n odd natural numbers are 1,3,5,7,9......2n-1

or (2-1),(4-1),(6-1),(8-1),(10-1)....... (2n-1)

4) The sum can be calculated as 2+4+6+8+10 +.... 2n +(-1-1-1-1-1......-1) n times

5) The sum of first n even natural numbers is n(n+1)

The sum of first n odd natural numbers in n(n+1)- n = n²

6) The ratio would be n(n+1)/n² or n+1/n