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  • The sum of the series 2 + 3 + 5 + 9 + 17..... upto n terms will be ?Option: 1 <img alt="2^n+n-1" src="https://learn.careers360.com/latex-image/?2%5En

The sum of the series 2 + 3 + 5 + 9 + 17..... upto n terms will be ?

Option: 1

2^n+n-1


Option: 2

2^n-n+1


Option: 3

2^{n-1}+n-1


Option: 4

2^{n-1}-n+1


Answers (1)

best_answer

Difference of consecutive terms are : 1, 2, 4, 8, .....which is a GP, so we can use method of difference

S_{n}=2+3+5+9+17.........+ T_{n} ...(i)\\ \text{ \ \ \ \ } S_{n}=\ \ \ \ 2+3+5+9............+T_{n-1}+T_{n} ... (ii)\\ \text{Equation (i)-(ii)}\\ 0=2+(1+2+4+8....+(T_{n}-T_{n-1}))-T_{n}\\ T_{n}=2+\frac{2^{n-1}-1}{2-1}\\ T_{n}=2^{n-1}+1\\ S_{n}=\sum_{1}^{n}T_{n}\\ S_n= (1+1) + (2+1)+(4+1).....\\S_n=(1+2+4+.....)+(1+1+1.....)\\S_{n}=\frac{2^{n}-1}{2-1}+n\\ S_{n}=2^n+n-1

Posted by

jitender.kumar

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