Sum of last eight coefficients in expansion of {(1 + x)^{15}} is

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7.Binomial Theorem

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The sum of the last eight coefficients in the expansion of ${(1 + x)^{15}}$ is

A

${2^{16}}$

B

${2^{15}}$

C

${2^{14}}$

D

None of these

Solution

(c) We have $^{15}{C_0} + {\,^{15}}{C_1} + … + {\,^{15}}{C_{15}} = {2^{15}}$

$ \Rightarrow \,\,\,2{(^{15}}{C_8} + {\,^{15}}{C_9} + … + {\,^{15}}{C_{15}}) = {2^{15}}$ $(\because \,{\,^n}{C_r} = {\,^n}{C_{n – r}})$

==> $^{15}{C_8} + {\,^{15}}{C_9} + … + {\,^{15}}{C_{15}} = {2^{14}}$

Standard 11

Mathematics

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