SOLUTION: show that the sum of the first N even natural numbers is equal to (1+1/N) times the sum of the first N odd natural numbers.

Question 6221: show that the sum of the first N even natural numbers is equal to (1+1/N) times the sum of the first N odd natural numbers.
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
You posted this question in wrong category.
The first N even natural numbers
Se= 2+ 4+...+ 2n =2(1+2+3+..+n) = 2* n(n+1)/2 = n(n+1)
The sum of the first N odd natural numbers
So= 1+3 +...+ (2n-1) [ arthemic series with common difference 2 ]
= n(1+2n-1)/2 = n^2.

We see that (1+ 1/n)So = (1+ 1/n)n^2 = n^2 + n = n(n+1) =Se
This completes the proof.
Kenny

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