The sum of last eight consecutive coefficient | vedclass

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Question

Sum of last eight coefficient are

${\rm{S}} = {15_{{C_8}}} + {15_{{{\rm{C}}_9}}} + {15_{{{\rm{C}}_{10}}}} +  \ldots  \ldots  + {15_{

Vedclass · Accepted Answer

$2^{14}$

Vedclass · Answer

Sum of last eight coefficient are

${\rm{S}} = {15_{{C_8}}} + {15_{{{\rm{C}}_9}}} + {15_{{{\rm{C}}_{10}}}} +  \ldots  \ldots  + {15_{{{\rm{C}}_{15}}}}$          .......$(i)$

${\rm{S}} = {15_{{C_7}}} + {15_{{C_6}}} + {15_{{C_5}}}, +  \ldots  \ldots  + {15_{{{\rm{C}}_0}}}$              ........$(ii)$

(We know that ${{{15}_{{{\rm{C}}_8}}} = {{15}_{{{\rm{C}}_7}}}}$)

equation $(i) + (ii)$

$2{\rm{S}} = {15_{{C_0}}} + {15_{{C_1}}} + {15_{{C_2}}} +  \ldots  \ldots  + {15_{{C_{15}}}}$

$\Rightarrow 2 \mathrm{S}=2^{15} \Rightarrow \mathrm{S}=2^{14}$

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

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