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