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What is the sum of first 10 terms of 1.2+2.2^2+3.2^3+.....

Option: 1

11.2^{11}+2


Option: 2

9.2^{11}+2


Option: 3

11.2^{11}-2


Option: 4

9.2^{11}-2


Answers (1)

best_answer

S=1.2+2.2^2+3.2^3+.....10.2^{10}

As common ratio of the corresponding GP is 2, so

2S= \,\,\,\,\,\,\,\,\,\,\,\,1.2^2+2.2^3+.................10.2^{11}

Subtracting these equations

-S=1(2+2^2+2^3+.....+2^{10})-10.2^{11}

S=10.2^{11}-(2+2^2+2^3+.....+2^{10})

S=10.2^{11}-2(2^{10}-1)

    =10.2^{11}-2^{11}+2= 9.2^{11}+2

 

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Rishi

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