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  • Find the sum of the coefficients of odd power of x in the expansion of (1+x+x2+x3)5Option: 1 512<div c

Find the sum of the coefficients of odd power of x in the expansion of (1+x+x2+x3)5

Option: 1

512


Option: 2

1024


Option: 3

32


Option: 4

64


Answers (1)

best_answer

Let \left ( 1+x+x^2+x^3 \right )^5=a_0+a_1x+a_2x^2+a_3x^3+\cdots\cdots+a_{15}x^{15}\\

putting x=1 and x=-1 alternatively, we have

\\a_0+a_1+a_2+a_3+\cdots\cdots+a_{15}=4^5..............(1)\\a_0-a_1+a_2-a_3+\cdots\cdots-a_{15}=0^5..............(2)

Subtracting (2) from (1)...

\\2(a_1+a_2+a_4+\cdots\cdots+a_{14})=4^5\\ or, \\(a_1+a_2+a_4+\cdots\cdots+a_{14})=\frac{4^5}{2}=512\\

hence option A is correct

Posted by

Rakesh

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