Convergence Tests
Curriculum and historical examination lineage for Convergence Tests under Unit 5 (Sequences and Series) of Calculus And Linear Algebra (21MAB101T) at SRMIST.
Historical appearance distribution across SRMIST Formative Tests (CT1, CT2) and University End Semester examinations.
Factual marks weightage of questions asked on this topic in historical examinations.
Question templates that recur across multiple examination cycles with similar conceptual stems.
“(a) Test the convergence of the series $\frac{1}{1.2.3} + \frac{3}{2.3.4} + \frac{5}{3.4.5} + ...$...”
“The series 1-\frac{1}{2^2}+\frac{1}{3^2}-\frac{1}{4^2}+...\infty is (A) Divergent (B) Convergent...”
“(a) Test the convergence of $\sum_{n=1}^{\infty} \left(\sqrt{n^2 + 1} - n\right)$. --- OR --- 25....”
“Answer part a or b (a) Test the convergence of 1 + \frac{1^2}{2^2} \frac{2^2}{3^3} +...”
“In D'Alembert's ratio test if \(\lim_{n\to\infty} \left(\frac{u_{n+1}}{u_n}\right) = l\), then the...”
Representative historical questions extracted directly from SRMIST examination papers.
The series \sum_{n=1}^\infty \frac{1}{n^{5/2}} is (A) Convergent (B) Divergent (C) Oscillates (D) Conditionally convergent
(a) Test the convergence of $\sum_{n=1}^{\infty} \left(\sqrt{n^2 + 1} - n\right)$. --- OR --- 25. Test the convergence of the series $\frac{1}{2} + \frac{4}{9}x + \frac{9}{28}x^2...
Test the convergence of the series $\frac{1}{2} + \frac{4}{9}x + \frac{9}{28}x^2 + .... + \frac{n^2}{1 + n^3}x^n + ...$ to $\infty, x > 0$. (b) Test the convergence of the series...
Answer part a or b (a) Test the convergence of 1 + \frac{1^2}{2^2} \frac{2^2}{3^3} + \frac{3^3}{4^4} + \dots \infty. --- OR --- 25. Prove that the series \sum_{n=1}^\infty...
Prove that the series \sum_{n=1}^\infty (-1)^{n+1} \frac{1}{n} is conditionally convergent, but not absolutely convergent.
Examinations where questions for Convergence Tests have appeared.
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