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The sum of last $30$ coefficients in the expansion of $(1+x)^{59}$ when expanded in ascending power of $x$ is ?

$\begin{array}{1 1} 2^{29} \\ 2^{28} \\ ^{60} C_{30} -2^{19} \\ 2^{58} \end{array}$

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  • $^nC_0+^nC_1+^nC_2+........^nC_n=2^n$
There are 60 terms in the expansion of $(1+x)^{59}$.
Let the sum of last 30 coefficients be $S$
Since $^nC_r=^nC_{n-r}$, we can write $S$ as
Adding both the $S$ we get
answered Oct 19, 2013 by rvidyagovindarajan_1

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