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  • Sum of first 10 terms of the series 1 + 3 + 7 + 15 + 31.....Option: 1 <img alt="2^{11}-12" src="https://learn.careers360.com/latex-image/?2%5E%7B11%7

Sum of first 10 terms of the series 1 + 3 + 7 + 15 + 31.....

Option: 1

2^{11}-12


Option: 2

2^{11}-10


Option: 3

2^{10}-10


Option: 4

None of these


Answers (1)

best_answer

\\S_{n}=1+3+7+15+31...\\ \text{Difference of first consecutive terms} = 2+4+8+16 \text{ , which is in G.P. with common ratio r = 2}\\\\So\,\,let\,\, T_{n}=ar^{n}+b= a.2^{n}+b\\ Put\ n=1,T_1=2a+b \Rightarrow 1 = 2a + b\\ Put\ n=2,T_2=4a+b \Rightarrow 3 = 4a + b \\ a=1,b=-1\\ T_{n}=2^n-1\\ S_{n}=\sum_{1}^{10}T_{n}\\ S_{n}=\frac{2(2^{10}-1)}{2-1}-10\\ S_{n}=2^{11}-12

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shivangi.shekhar

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