The positive integral value of \( n \) such that \( 1 \times 2^{1}+2 \times 2^{2} \) \( +3 \time...

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The positive integral value of \( n \) such that \( 1 \times 2^{1}+2 \times 2^{2} \) \( +3 \times 2^{3}+4 \times 2^{4}+\cdots+n \times 2^{n}=2+2^{n+5} \), is
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