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Consider the expansion of $(1+\mathrm{x})^{2 \mathrm{n}+1}$
The sum of the coefficients of all the terms in the expansion is
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The sum of the coefficients of all the terms in the expansion is
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The correct answer is:
$2 \times 4^{\text {n }}$
Sum of all coefficient
$={ }^{(2 \mathrm{n}+1)} \mathrm{C}_{0}+{ }^{(2 \mathrm{n}+1)} \mathrm{C}_{1}+\ldots \ldots .+{ }^{(2 \mathrm{n}+1)} \mathrm{C}_{2 \mathrm{n}+1}$
$=(1+1)^{2 \mathrm{n}+1}=2^{(2 \mathrm{n}+1)}=2.2^{2 \mathrm{n}}=2.4^{\mathrm{n}}$
$={ }^{(2 \mathrm{n}+1)} \mathrm{C}_{0}+{ }^{(2 \mathrm{n}+1)} \mathrm{C}_{1}+\ldots \ldots .+{ }^{(2 \mathrm{n}+1)} \mathrm{C}_{2 \mathrm{n}+1}$
$=(1+1)^{2 \mathrm{n}+1}=2^{(2 \mathrm{n}+1)}=2.2^{2 \mathrm{n}}=2.4^{\mathrm{n}}$
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