jee-main 2021 Q83

jee-main · India · session3_20jul_shift2 Partial Fractions

For $k \in N$, let $\frac { 1 } { \alpha ( \alpha + 1 ) ( \alpha + 2 ) \ldots ( \alpha + 20 ) } = \sum _ { K = 0 } ^ { 20 } \frac { A _ { k } } { \alpha + k }$, where $\alpha > 0$. Then the value of $100 \left( \frac { A _ { 14 } + A _ { 15 } } { A _ { 13 } } \right) ^ { 2 }$ is equal to $\underline{\hspace{1cm}}$.

For $k \in N$, let $\frac { 1 } { \alpha ( \alpha + 1 ) ( \alpha + 2 ) \ldots ( \alpha + 20 ) } = \sum _ { K = 0 } ^ { 20 } \frac { A _ { k } } { \alpha + k }$, where $\alpha > 0$. Then the value of $100 \left( \frac { A _ { 14 } + A _ { 15 } } { A _ { 13 } } \right) ^ { 2 }$ is equal to $\underline{\hspace{1cm}}$.

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