Difference between revisions of "Telescoping series"
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In mathematics, a telescoping series is a series whose partial sums eventually only have a finite number of terms after cancellation. | In mathematics, a telescoping series is a series whose partial sums eventually only have a finite number of terms after cancellation. | ||
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| + | ==Problems== | ||
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| + | ===Intermediate=== | ||
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| + | *Find the value of <math>\sum_{k=2}^{\infty} \left( \zeta(k) - 1 \right),</math> where <math>\zeta</math> is the [[Riemann zeta function]] <math>\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}.</math> | ||
{{stub}} | {{stub}} | ||
Revision as of 12:07, 20 March 2022
In mathematics, a telescoping series is a series whose partial sums eventually only have a finite number of terms after cancellation.
Problems
Intermediate
- Find the value of
where 
is the Riemann zeta function 
where 
is the 
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