matematika



Calculate the sum

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Calculate the sum

Postby Math Tutor » Thu Feb 21, 2013 2:58 pm

Calculate the sum:
\frac{1}{1\cdot2}+\frac{1}{2\cdot2}+\frac{1}{3\cdot2}+...+\frac{1}{n(n+1)}


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Re: Calculate the sum

Postby Guest » Fri Feb 22, 2013 6:23 am

Are you sure you typed the question correctly? I don't see the pattern of your terms.

The start of your sum are the first three values of the sequence \frac{1}{n\cdot 2} which doesn't match the last term \frac{1}{n(n+1)}.

If you meant \frac{1}{1\cdot 2} + \frac{1}{2\cdot 3} + \frac{1}{3\cdot 4} + \ldots + \frac{1}{n(n+1)}
the answer is given below
Spoiler: show
\frac{1}{r(r+1)} = \frac{1}{r} - \frac{1}{r+1}
so
\frac{1}{1\cdot 2} + \frac{1}{2\cdot 3} + \frac{1}{3\cdot 4} + \ldots + \frac{1}{n(n+1)} = (\frac{1}{1} - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + \ldots + (\frac{1}{n} - \frac{1}{n+1}) = 1 - \frac{1}{n+1}


R. Baber
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Re: Calculate the sum

Postby Math Tutor » Fri Feb 22, 2013 1:34 pm

Perfect!
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