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Find the coefficient of x 101 in the expansion 1 + (1+x) + (1+x) 2 + ------------------- + (1+x) 2011

Find the coefficient of x101 in the expansion 1 + (1+x) + (1+x)2 + ------------------- + (1+x)2011

Grade:11

1 Answers

moumi roy
91 Points
7 years ago
series is in gp.so there sum can fetch us the result.\sum 1+\left ( 1+x\right )+\left ( 1+x\right )^{2}.....+\left ( 1+x\right )^{2011}\Rightarrow 1*[\frac{(1+x)^{2012}-1}{x}]\Rightarrow \frac{(1+x)^{2012}}{x}-\frac{1}{x}
coifficient of x102 is needed of the first part _{102}^{2012}\textrm{c}.hope this is the needed answer

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