SOLUTION: Prove that log 3=(log 2)+ (1/2)-(1/8)+(1/24)-(1/64)+....and so on.

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Question 464432: Prove that log 3=(log 2)+ (1/2)-(1/8)+(1/24)-(1/64)+....and so on.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
This is true if and only if

,

because it will satisfy the logarithm identity . However, the above series is equal to ln 3/2. If you know the Taylor series for ln x centered at 1



We can replace x = 3/2 and get a true result. Hence the original equation is true.