Question

If $a_r$ is the coefficient of $x^{10-r}$ in the Binomial expansion of $(1+x)^{10}$, then $\displaystyle\sum_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2$ is equal to

• A. 3025
• B. 1210
• C. 5445
• D. 4895

Answer 1

Answer: (B)

1210

Answer 2

ar​=10C10−r​=10Cr​
⇒r=1∑10​r3(10Cr−1​10Cr​​)2=r=1∑10​r3(r11−r​)2=r=1∑10​r(11−r)2
=r=1∑10​(121r+r3−22r2)=1210