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Which is the first term of the series 2, 4, 8, 16... where the sum of terms is greater...

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theking00 | Student, Kindergarten | eNoter

Posted April 29, 2013 at 8:29 AM via web

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Which is the first term of the series 2, 4, 8, 16... where the sum of terms is greater than 10000

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 29, 2013 at 8:36 AM (Answer #1)

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The series 2, 4, 8, 16 is a geometric series as the result of dividing each term from the previous term is 2, `4/2 = 8/4 = 16/8 = 2` .

The nth term of the series is `t_n = 2*2^(n-1)`

The sum of n terms of this series is (2*(2^n - 1))/(2 - 1) = 2*(2^n - 1)

If `2*(2^n - 1) > 10000`

`(2^n - 1) > 5000`

`2^n > 5001`

The minimum value of n for which `2^n > 5001` is n = 13

The sum of all terms till the 13th term is greater than 10000.

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