Let S=n=0nαn where |α|<1. the value of α in the range 0<α<1, such that S=2α is  _______.

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s=α+2α2+3α3+.αs=α2+2α3+3α4+.s(1α)=α+α2+α3+.=α1αs=α(1α)2=2α(1α)2=121α=12α=0.2929
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