Telescoping Series Calculator
Calculate telescoping series sums where consecutive terms cancel out.
Series Type
Series:
β [1/n - 1/(n+1)] from n=1 to n=10
Telescoping Sum
0.90909091
Simplification
= 1/1 - 1/11
Term Cancellation
Remaining: 1/1, -1/11
Cancelled: 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10
Individual Terms (first 10)
What is a Telescoping Series?
A telescoping series is a series where most terms cancel with preceding or following terms, leaving only a few terms to evaluate. This makes finding the sum much simpler.
Example: β(1/n - 1/(n+1))
(1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + ...
= 1/1 - 1/(n+1) = 1 - 1/(n+1)
Key Technique
Use partial fractions to decompose terms into differences that telescope.
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
Formula Source: Handbook of Mathematical Functions
by Abramowitz & Stegun