If 23 +43+63+............+(2n)3 =kn2(n+1)2, then k=?

If 2+43+63+............+(2n)3 =kn2(n+1)2, then k=?

  • 1 answers

Shruti Dadhwal 3 years, 8 months ago

The sum of cubes of even numbers is equal to 2 n^2 (n+1)^2

So 2^3+ 4^3+ 6^3 +........+2n^2 = 2n^2(n+1)^2 

2 n^2 (n+1)^2  = k n^2 (n+1) ^2

Cancelling the common terms, we get 

k=2

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