If C_r=^10C_r then the value of {C}_{0}+3\cdot{C}_{1}+5\cdot{C}_{2}+. . ....+21\cdot{C}_{10}=

AP ICET 2016 Paper

Question : 137 of 200

Marks: +1, -0

C_r=^10C_r

then the value of

{C}_{0}+3⋅{C}_{1}+5⋅{C}_{2}+. . ....+21⋅{C}_{10}=

Solution:

Given :

Cr=^{10}C_r

⇒n=10

C_0+3C_1+5C_2+............+21C_10

It can be represented by the series

∑↙{n=0}↖{10}(1+2n)c_{n}

$∑↙{n=0}↖{10}c_{n}+2∑↖{10}↙{n=0}nC_n=2^10+2×10×2^9$

=2^10(1+10)=11(2^10)

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