Sum of the given series will be

Calculus Level 3

\[\large \frac 7{2^3} + \frac {19}{6^3} + \frac {37}{12^3} + \frac {61}{20^3} + \cdots = \ ? \]

Note that

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

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

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