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What is the sum of this series equal to in the limit?

2/100, 4/10000, 8/10^6, 16/10^8, 32/10^10, ...

Yeah....its a simple geometric series....but it is kinda interesting when you multiply each term by 7 and see what the sum is equal to.

## 7 answers to this question

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from what I can tell the nth term is

2n/102n

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I forgot the formulae of geometric series..and i am too lazy to get help from the net

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from what I can tell the nth term is

2n/102n

That's right, though it can be simplified to a simple power of a fraction.

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What is the sum of this series equal to in the limit?

2/100, 4/10000, 8/10^6, 16/10^8, 32/10^10, ...

Yeah....its a simple geometric series....but it is kinda interesting when you multiply each term by 7 and see what the sum is equal to.

The sum is 1/49.

Multiplying by 7 gives 1/7.

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the sum is 1/49...if you multiply it with 7, it will be 1/7...if you multiply with 72 it will be 1

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the sum is 1/49...if you multiply it with 7, it will be 1/7...if you multiply with 72 it will be 1

So, echo ... guess you looked the formula up after all.

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the decimal expansion of 1/7 = .142857142857142857...

14 = (7*2)

28 = (7*4)

56 = (7*8)

112 = (7*16)

etc.

At least it is an easy way to remember what 1/7th is equal to.

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