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VerifyConvergence

VerifyConvergence
is an option to Sum, NSum, and similar functions that specifies whether convergence checking should be done.

With the default setting VerifyConvergence->True, convergence is automatically checked for infinite sums and similar constructs.

With VerifyConvergence->False, convergence is not explicitly checked, and results may correspond to various regularized forms.

With the default setting VerifyConvergence->True, setting GenerateConditions->True will generate conditions for convergence.

By default Sum will verify convergence:

Setting

False will avoid the verification step:

In this case, this result corresponds to a regularized version of the sum:

By default Sum will verify convergence:

Out[1]=

Setting

False will avoid the verification step:

Out[2]=

In this case, this result corresponds to a regularized version of the sum:

Out[3]=