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If r > 1, then the series diverges. If r = 1, the root test is inconclusive, and the series may converge or diverge. The root test is stronger than the ratio test: whenever the ratio test determines the convergence or divergence of an infinite series, the root test does too, but not conversely. [1]
Taxes can be complicated, and it's not uncommon to make a mistake on a tax return. The Internal Revenue Service recognizes this and allows taxpayers to amend their returns to correct errors they...
For filing the regular tax return, in addition to the standard Form 1040, there are currently three variants: the 1040-NR 1040-SR, and 1040-X. Form 1040X, 2011. Form 1040-NR is used by taxpayers who are considered "non-resident aliens" for tax purposes. Form 1040-SR may be used by taxpayers who are 65 or older.
The more general class of p-series, =, exemplifies the possible results of the test: If p ≤ 0, then the nth-term test identifies the series as divergent. If 0 < p ≤ 1, then the nth-term test is inconclusive, but the series is divergent by the integral test for convergence.
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In mathematics, the comparison test, sometimes called the direct comparison test to distinguish it from similar related tests (especially the limit comparison test), provides a way of deducing whether an infinite series or an improper integral converges or diverges by comparing the series or integral to one whose convergence properties are known.
In mathematics, the limit comparison test (LCT) (in contrast with the related direct comparison test) is a method of testing for the convergence of an infinite series. Statement [ edit ]