Sum of the given series will be

Calculus Level 3

723+1963+37123+61203+= ?\large \frac 7{2^3} + \frac {19}{6^3} + \frac {37}{12^3} + \frac {61}{20^3} + \cdots = \ ?

Note that

  • In the sequence 7,19,37,61,7,19,37,61,\ldots, the difference between each consecutive terms follows an arithmetic progression.

  • In the sequence 2,6,12,20,2,6,12,20, \ldots,the difference between each consecutive terms follows an arithmetic progression as well.

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