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Question

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then write the value of k.

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Solution

It is given that the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers. 2+4+6...2n=k(1+3+5...n)2(1+2+3...n)=k(1+3+5...n)2×n(n+1)2=k(1+3+5...n)n(n+1)2=k×n2sum of first odd natural numbers is n2n(n+1)n2=kHence, k=n+1n


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