Question

$(1 + x)^{15} = C_{0} + C_{1}x + C_{2}x^{2} + ...... + C_{15}x^{15},$ divisible ($C_{2} + 2C_{3} + 3C_{4} + .... + 14C_{15} =$).

• A. By $13.2^{14} - 1$
• B. By $\frac{2^{n} - 1}{n + 1}$
• C. By $\frac{2^{n}}{n}$
• D. All of these

Answer 1

Answer: (B)

By $\frac{2^{n} - 1}{n + 1}$

Answer 2

$T_{r + 1} = \frac{n(n - 1)(n - 2)......(n - r + 1)}{r!}(x)^{r}$

∴ $n - r + 1 < 0$

From above it is clear that $r > \frac{32}{5}$is divisible by x².