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SumTools[DefiniteSum]

  

Telescoping

  

compute closed forms of definite sums using telescoping method

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Telescoping(f, k=m..n)

Parameters

f

-

expression; specified summand

k

-

name; summation index

m, n

-

expressions or integers

Description

• 

The Telescoping(f, k=m..n) command computes a closed form of the definite sum of f over the specified range of k using telescoping method, or Newton-Leibniz's formula, that is, it first computes a closed form of the corresponding indefinite sum.

Examples

withSumToolsDefiniteSum:

Fbinomial2n2k,nk24k2k2k+1binomial2k,k1

F2n2knk24k2k2k+12kk

(1)

k=1nF=TelescopingF,k=1..n

k=1n2n2knk24k2k2k+12kk=2n2n18n+42n+1

(2)

See Also

SumTools[DefiniteSum]

SumTools[DefiniteSummation]

SumTools[IndefiniteSummation]

SumTools[Summation]