JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(a_r\) is the coefficient of \(x^{10-r}\) in the Binomial expansion of \((1+x)^{10}\), then \(\sum \limits_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2\) is equal to
- A \(4895\)
- B \(1210\)
- C \(5445\)
- D \(3025\)
Answer & Solution
Correct Answer
(B) \(1210\)
Step-by-step Solution
Detailed explanation
\(a _{ r }={ }^{10} C _{10- r }={ }^{10} C _{ r }\) \(\Rightarrow \sum \limits_{ r =1}^{10} r ^3\left(\frac{{ }^{10} C _{ r }}{{ }^{10} C _{ r -1}}\right)^2=\sum \limits_{ r =1}^{10} r ^3\left(\frac{11- r }{ r }\right)^2=\sum \limits_{ r =1}^{10} r (11- r )^2\)…
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