Grade 11Algebra
Find the coefficient of x101 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
1 Answer
moumi roy
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}](http://latex.codecogs.com/gif.latex?%5Csum%201+%5Cleft%20%28%201+x%5Cright%20%29+%5Cleft%20%28%201+x%5Cright%20%29%5E%7B2%7D.....+%5Cleft%20%28%201+x%5Cright%20%29%5E%7B2011%7D%5CRightarrow%201*%5B%5Cfrac%7B%281+x%29%5E%7B2012%7D-1%7D%7Bx%7D%5D%5CRightarrow%20%5Cfrac%7B%281+x%29%5E%7B2012%7D%7D%7Bx%7D-%5Cfrac%7B1%7D%7Bx%7D)
coifficient of x102 is needed of the first part 
.hope this is the needed answer
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