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

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

    • Posted by Amulya Chukka 7 years, 4 months ago

    CBSE > Class 11 > Mathematics
    • 1 answers

    Shruti Dadhwal 7 years, 4 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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