Find the sum of the following series to infinity : (i) 1−13+132−13

1.	Find the sum of the following series to infinity : (i) 1−13+132−133+134+....∞ (ii) 8+4√2+4+....∞ (iii) 25+352+253+354+.....∞. (iv) 10 - 9 + 8.1 - 7.29 + ...... ∞ (v) 13+152+133+154+135+156+.....∞
Answer» Find the sum of the following series to infinity : (i) $1 - \frac{1}{3} + \frac{1}{3^{2}} - \frac{1}{3^{3}} + \frac{1}{3^{4}} + . . . . \infty$ (ii) $8 + 4 \sqrt{2} + 4 + . . . . \infty$ (iii) $\frac{2}{5} + \frac{3}{5^{2}} + \frac{2}{5^{3}} + \frac{3}{5^{4}} + . . . . . \infty$ . (iv) 10 - 9 + 8.1 - 7.29 + ...... $\infty$ (v) $\frac{1}{3} + \frac{1}{5^{2}} + \frac{1}{3^{3}} + \frac{1}{5^{4}} + \frac{1}{3^{5}} + \frac{1}{5^{6}} + . . . . . \infty$

Find the sum of the following series to infinity : (i) 1−13+132−133+134+....∞ (ii) 8+4√2+4+....∞ (iii) 25+352+253+354+.....∞. (iv) 10 - 9 + 8.1 - 7.29 + ...... ∞ (v) 13+152+133+154+135+156+.....∞

Answer»

Find the sum of the following series to infinity :

(i) $1 - \frac{1}{3} + \frac{1}{3^{2}} - \frac{1}{3^{3}} + \frac{1}{3^{4}} + . . . . \infty$

(ii) $8 + 4 \sqrt{2} + 4 + . . . . \infty$

(iii) $\frac{2}{5} + \frac{3}{5^{2}} + \frac{2}{5^{3}} + \frac{3}{5^{4}} + . . . . . \infty$ .

(iv) 10 - 9 + 8.1 - 7.29 + ...... $\infty$

(v) $\frac{1}{3} + \frac{1}{5^{2}} + \frac{1}{3^{3}} + \frac{1}{5^{4}} + \frac{1}{3^{5}} + \frac{1}{5^{6}} + . . . . . \infty$