Find the sum of the series (4^k-3^k)/(5^k) from k=0 to infinity
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Find the sum of the series (4^k-3^k)/(5^k) from k=0 to infinity

[From: ] [author: ] [Date: 12-06-12] [Hit: ]
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Do I make this into a limit and use natural logs? Or am I way off base? Please show steps!

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Σ (4/5)^k - Σ (3/5)^k

The first is a geometric series with common ratio r=4/5 and first term 1
sum of series 1 = a/(1-r) = 1/(1-4/5) = 5
sum of the second series = 1/(1-3/5) = 5/2

5-5/2 = 5/2
Sum = 2.5
1
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