Mathematics-I (3110014)

Maths-I-3110014

Convergence and divergence of sequences

BE | Semester 1 Unit : Convergence and divergence of sequences

Q2 (a) Winter-2019 Test the convergence of the series $(\frac{1}{3}) + {(\frac{2}{5})}^{2} + {(\frac{3}{7})}^{3} + . . . + {(\frac{n}{2 n + 1})}^{n} + . . .$

Unit : Convergence and divergence of sequences

Q3 (a) Winter-2019 Test the convergence of the series $\frac{1}{1^{2}} - \frac{1}{2^{2}} + \frac{1}{3^{2}} - \frac{1}{4^{2}} + . . .$ .

Unit : Convergence and divergence of sequences

Q4 (b) Winter-2019 Express $f (x) = 2 x^{3} + 3 x^{2} - 8 x + 7$ in terms of $(x - 2)$ .

Unit : Convergence and divergence of sequences

Q4 (c) Winter-2019 Test the convergence of the series $\frac{x}{1 \cdot 2} + \frac{x^{2}}{3 \cdot 4} + \frac{x^{3}}{5 \cdot 6} + \frac{x^{4}}{7 \cdot 8} + . . .$ .

Unit : Convergence and divergence of sequences

Q5 (b) Winter-2019 Test the convergence of the series $\sum_{n = 1}^{\infty} \frac{\sqrt{n}}{n^{2} + 1}$ .

Unit : Convergence and divergence of sequences