Question

(it) Show that the sum of first n even number is equal to (1+1/n)
times the sum of first
n odd numbers.​

Answer 1

Answer:

Sum (n) of even number= n-1/n odd number

Sum of first (n) even natural number

So= 2+4+....+2n=2(1+2+3+....+n) =2*n(n+1)/2=(n+1)

The sum of the first n odd natural number

So=1+3+...+(2n-1)

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

We see that

(1+1/n) So = (1+1/n^2=n^2+n=n(n+1)

Hence proved