106it is simply -\sum_{r=1}^{50}{r^2\frac{C_{r}}{C_{r-1}}}
Came in roorkee mains.
Find the coefficient of x49 in the polynomial
\left(x-\frac{C_{1}}{C_{0}} \right)\left(x-2^{2} \frac{C_{2}}{C_{1}}\right)\left(x-3^{2}\frac{C_{3}}{C_{2}} \right).....\left(x-50^{2}\frac{C_{50}}{C_{49}} \right)
ans -----> 25( 1666 - 51 n )
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2 Answers
62More simply,
r^2\times \frac{C_r}{c_{r-1}}=r^2\times \frac{\frac{n!}{r!(n-r)!}}{\frac{n!}{(r-1)!(n+1-r)!}}=r^2\times \frac{(r-1)!(n+1-r)!}{r!(n-r)!}=r^2\times \frac{(n+1-r)}{r}
=r\times(n+1-r)
