If a r is the coefficient of x^(10-r) in the Binomial expansion of (1 + x)¹⁰, then Σ r = 1 ¹⁰ r³(a r /(a r - 1))² is equal to

Binomial Theorem and Its Simple Applications: JEE Main 2023 Mathematics question

JEE Main 2023 · 25 Jan, Morning shift · Q3005

JEE Main 202325 Jan, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

a_r

is the coefficient of

x^{10-r}

in the Binomial expansion of

(1 + x)^{10}

, then

\sum\limits_{r = 1}^{10} {{r^3}{{\left( {{{{a_r}} \over {{a_{r - 1}}}}} \right)}^2}}

is equal to