For , let 1 ( +1)( +2) ( +20) = _ k=0 ^ 20 A_k +k where . Then the value of is equal…

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

For

k \in \mathbb{N}

, let

\frac{1}{\alpha(\alpha+1)(\alpha+2)\dots(\alpha+20)} = \sum_{k=0}^{20} \frac{A_k}{\alpha+k}

where

\alpha > 0

. Then the value of

100 \left( \frac{A_{14} + A_{15}}{A_{13}} \right)^2

is equal to ____.