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For a geometric question:

[From: ] [author: ] [Date: 11-12-21] [Hit: ]
QED-Jacky,Thanks for picking my answer as the best.For any infinite geometric series, sum = a(1)/(1-r), where a(1) is the first term, r is the common ratio.......
Prove that

1-1/√2+1/2-1/2√2+...=2-√2

-
1-1/√2+1/2-1/2√2+...
= 1/(1 + 1/√2)
= √2/(√2 + 1)
= √2*(√2 - 1)
= 2-√2

QED

-
Jacky,
Thanks for picking my answer as the best.
For any infinite geometric series, sum = a(1)/(1-r), where a(1) is the first term, r is the common ratio.

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