p-Test — Study Resources & PYQs
Convergence test for positive term series using the p-series criterion.
- Estimated study time: 30 minutes
Study resources
- 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.
- 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 - P-Series and Geometric Series Test | By GP Sir (Video) — Lecture deriving the p-series (and geometric series) test for convergence, with worked examples showing how to read off the value of p.
- Multivariable Calculus playlist contents - GP Sir (Class Central index) (Article) — This index lists 'Non Linear PDE Standard Form-I, II, III' and 'Standard form-IV | Clairaut's Form' as separate lectures, plus Lagrange form and Charpit's method. Use it to open exactly the standard…
p-Test previous year questions
- (a) Discuss the convergence or divergence of the series $\sum \left(\frac{1+n}{n}\right)^n$ (b) Find the interval of convergence of the series: $1 + x + \frac{…
- Discuss the convergence of the series: $1^p + \left(\frac{1}{2}\right)^p + \left(\frac{1.3}{2.4}\right)^p + \left(\frac{1.3.5}{2.4.6}\right)^p + \dots$
- Show that the series $\sum u_n$ is divergent, where $u_n = \frac{n(n + 1)}{(n + 2)(n + 3)(n + 4)}$
Taught in these subjects
- ENGINEERING MATHEMATICS-II — BMAT21 · Government College of Engineering and Technology, Jammu
- ENGINEERING MATHEMATICS-II — BMAT21 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-II — BMAT21 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-II — BST1201 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-II — BST1201 · Government College of Engineering and Technology, Jammu