SUM OF MISCELLANE OF MISCELLANEOUS ...
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SUM OF MISCELLANE OF MISCELLANEOUS SERIES, INEQUALITIES SARITHMETIC MEAN OF MTH POWER 18 Sum of the series 1+ 3+ 7 + 15 + 31+ .... to n terms is- (A) 21 -2-n (B) 2n+1+2+n (C) 2n+1-3=n (D) None of these

JEE/Engineering Exams
Maths
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( begin{aligned} & 1+3+7+15+-n =& 2 &(2-1)+left(2^{2}-1right)+left(2^{3}-1right)+frac{1}{2}-left(2^{n}-1right) &=left(2+2^{1}+2^{1}+-2right)-7 &=int frac{2left(2^{n}-1right)}{(2-1)}-n &=1 quad 2^{n+1}-2-n Rightarrow mid 2^{n+1}-n-2 end{aligned} )
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