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Question
How many terms of the series 1 + 2 + 4 + .... has the sum 511?
Sum
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Solution
Sn = 511
a = 1
r = `2/1`
= 2 > 1
n = ?
`S_n = (a (r^n - 1))/(2 - 1) = 511`
= `(1 ((2)^2 - 1))/(2 - 1) = 511`
= 2n − 1 = 511
⇒ 2n = 512
⇒ 29 = 512
n = 9
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