# Diwali Blast!!!

Calculus Level 4

Let

$$\displaystyle S = \frac{3}{2^{2}\times 1 \times 2} + \frac{4}{2^{3}\times 2 \times3} + \frac{5}{2^{4}\times 3 \times 4} + \frac{6}{2^{5} \times 4 \times 5} + \ldots$$

Then the value of

$$\displaystyle S^{-12}$$ is ?

Note

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

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