Leibnitz Test for Alternating Series — Study Resources & PYQs
Leibnitz criterion for convergence of alternating series.
- Estimated study time: 30 minutes
Study resources
- Paul's Online Notes - Alternating Series Test & Absolute Convergence (Article) — From this chapter page, open the Alternating Series Test section. Explains the two Leibnitz conditions with examples such as the alternating harmonic series.
- Infinite Series (Convergence & Divergence) - GP Sir (Video) — Contains a dedicated lecture on the Leibnitz test, with the standard examples such as the alternating harmonic series.
- Wikipedia - Alternating series test (Article) — Statement and history of the Leibniz/alternating-series test: an alternating series converges if its terms decrease monotonically in absolute value to zero.
- Wikipedia - Convergence tests (Article) — One-page summary table of all convergence tests including p-test, ratio, root, Raabe, Gauss and logarithmic. Useful as a last-minute formula sheet to revise all conditions together.
- Infinite Series | Necessary Condition & P-Series Test - GP Sir (Video) — Explains the necessary (but not sufficient) condition for convergence and then derives the p-test, showing exactly when sum 1/n^p converges. Watch this before any other test.
- MIT OpenCourseWare — Fourier Series and Partial Differential Equations (Article) — MIT course materials covering Fourier series and partial differential equations.
Leibnitz Test for Alternating Series previous year questions
- Solve the following ordinary differential equations: (a) $xydy - y^2dx = (x^2 + y^2)dy$ (b) $(D^2 - 2D + 1)y = x\sin x$
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- Let $T: R^2 \to R^3$ be defined as $T(x, y) = (x + y, x - y, y)$ for any $x, y \in R$. Then show that $T$ is linear. Also find a basis and dimension of its ran…
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