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Calculus Level 4

Let

S=322×1×2+423×2×3+524×3×4+625×4×5+\displaystyle S = \frac{3}{2^{2}\times 1 \times 2} + \frac{4}{2^{3}\times 2 \times3} + \frac{5}{2^{4}\times 3 \times 4} + \frac{6}{2^{5} \times 4 \times 5} + \ldots

Then the value of

S12\displaystyle S^{-12} is ?

Note

  • Try to find the nthn^{th} term of the series

  • Happy Diwali to all

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