Duday P.

asked • 07/24/16

Geometric Series

1. Find the sum: (1/√1 + √2) + (1/√2 + √3) + (1/√3 + √4) + ... + (1/√99 + √100)

Inactive Tutor

The given series is no way a geometric progression series. Geometric progression series is defined by each pair of consecutive terms have the same ratio between them. The consecutive pairs of terms in the given series does not have a common ratio.

BUT this is sum of twp different series.

Given that, S=(1/√1 + √2) + (1/√2 + √3) + (1/√3 + √4) + ... + (1/√99 + √100), where
S1= 1/√1 +1/√2 +1/√3 +... +1/√99 and S2=√2+ √3 + √4+ ... +√100
S1=n=1∑99(1/√n) and S2=n=2∑100(√n) where n is number of a natural numbers in the series and for both S1 and S2 n=99
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07/24/16

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