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How do you find the sum of an infinite sequence with different ratios?
Wiki User
∙ 11y ago
If you are talking about a geometric sequence,where each term if found by multiplying the previous term by a ratio (r), so you might have something like:
r0 + r1 + r2 + r3 + .... + rn. This series sum is equal to 1/(1-r) if |r|< 1. See related link on Wolfram MathWorld.
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True, but here the ratio between successive terms is always is the same: r. The question specifically excluded such sequences.
There is not enough space or time to deal with this here. But, to summarise crudely, if every term in the sequence is positive then the series is monotonic increasing. If then you can find a number such that the series is bounded by that number then it must converge. This process does not, of itself, give you the infinite sum but it tells you that such a sum does exist.
Wiki User
∙ 11y ago
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