- #1

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ran this in Matlab and n,m to 2:1000 =0.9990, and n,m 2:10000 =0.9999, so it does appear to converge to 1

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- #1

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- 870

ran this in Matlab and n,m to 2:1000 =0.9990, and n,m 2:10000 =0.9999, so it does appear to converge to 1

- #2

mjc123

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What is the sum of these sums from n = 2 to ∞?

- #3

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- #4

mjc123

Science Advisor

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Playing with Wolfram Alpha? You're not familiar with the result

a(1+r+r^{2}...) = a/(1-r) ?

a(1+r+r

- #5

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The series ##\sum_{n=2}^\infty (n(n-1))^{-1} = \sum_{n=2}^\infty \left( \frac{1}{n-1} - \frac1n \right)## does sum to 1 because ##\sum_{n=2}^N \left( \frac{1}{n-1} - \frac1n \right) =1-1/N##

- #6

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Yes, for some reason it took me a while to see it as a geometric series instead of a p-series

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