The sum of the last 30 coefficients in the ex | vedclass

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(B) The expansion of $(1+x)^{59}$ has $59+1 = 60$ terms.Let the coefficients be $C_0, C_1, C_2, \dots, C_{59}$.The sum of all coefficients is $\sum_{r

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$2^{58}$

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(B) The expansion of $(1+x)^{59}$ has $59+1 = 60$ terms.Let the coefficients be $C_0, C_1, C_2, \dots, C_{59}$.The sum of all coefficients is $\sum_{r=0}^{59} C_r = (1+1)^{59} = 2^{59}$.Since $C_r = C_{59-r}$, the sum of the first $30$ coefficients is equal to the sum of the last $30$ coefficients.Let $S$ be the sum of the last $30$ coefficients.Then $2S = \sum_{r=0}^{59} C_r = 2^{59}$.Therefore, $S = \frac{2^{59}}{2} = 2^{58}$.

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

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