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1+3+7+15+31+........to n terms 

Option: 1

2^{n+1}-n


Option: 2

2^{n+1}-n-2


Option: 3

2^{n}-n-2


Option: 4

None of these


Answers (1)

best_answer

S_{n}=1+3+7+15+31+.......+T_{n}\\ .\,\,\,\,\,\,\,S_{n}=\,\,\,\,\,\,\,\,\,\,1+3+7+.................+T_{n-1}+T_n\\ Subtracting\\ 0=1+2+4+8...(n\,terms) - T_n\,\,\\ T_n=1\times \frac{(2^n-1)}{2-1}\\ =(2^n-1)\\ S_{n}=\sum_{1}^{n} T_{n} =\sum_{1}^{n} 2^n-\sum_{1}^{n}1\\ =2(2^n-1)-n\\ =2^{n+1}-(n+2)

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SANGALDEEP SINGH

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