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7.Binomial Theorem
hard
The coefficient of ${x^{100}}$ in the expansion of $\sum\limits_{j = 0}^{200} {{{(1 + x)}^j}} $ is
A
$\left( \begin{array}{l}200\\100\end{array} \right)$
B
$\left( \begin{array}{l}201\\102\end{array} \right)$
C
$\left( \begin{array}{l}200\\101\end{array} \right)$
D
$\left( \begin{array}{l}201\\100\end{array} \right)$
Solution
(a) ${T_{r + 1}} = {\,^{200}}{C_r}{(1)^{200 – r}}.{(x)^r}$
Hence coefficient of ${x^{100}} = {\,^{200}}{C_{100}} = \left( \begin{array}{l}200\\100\end{array} \right)$.
Standard 11
Mathematics
