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September 24th, 2008, 06:55 PM   #1
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Target Values & Series

Consider the series 1-(1/2)+(1/3)-(1/4)+...+((-1)^(k-1))/k+...prove that there is a target value T (whether we know what it is or not) which is the VALUE of this series.

Can anyone help me out?

I have a value of 2/3 and where n=10 value is within .001. But not quite sure what this question is asking me to do???
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September 25th, 2008, 03:04 AM   #2
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Re: Target Values & Series

The problem asks you to show that this series is convergent. In order to do this, you can use the alternate series theorem: consider sequence (u_n) of real numbers such that (-1)^(n+1)u_n >=0, limit u_n = 0 and (|u_n|) is decreasing. Then sum(u8n) converges.
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