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What is the sum of n terms of the series 4, 6, 10, 18...

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theta123 | Student, Kindergarten | Salutatorian

Posted June 10, 2013 at 6:32 AM via web

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What is the sum of n terms of the series 4, 6, 10, 18...

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 10, 2013 at 6:39 AM (Answer #1)

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The sum of n terms of the series 4, 6, 10, 18 ... has to be determined.

4 = 2 + 2

6 = 2^2 + 2

10 = 2^3 + 2

18 = 2^4 + 2

The nth term of the series is `t_n` = 2^n + 2

The sum of n terms is 2^1 + 2^2 ... 2^n + 2*n

2^1 + 2^2 ... 2^n is a geometric series, the sum of n terms is (2*(2^n - 1))/(2 - 1) = 2^(n+1) - 2

This gives the sum of n terms of the given series as 2^(n+1) +2*(n - 1)

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