• # question_answer The sum of the series: $1+\frac{3}{2}+\frac{5}{4}+\frac{7}{6}+......\infty$is equal to A) 3e                    B) 2e             C) e                                  D) 5e

Solution :

[c]$1+\frac{3}{2}+\frac{5}{4}+\frac{7}{6}+......to\,\,\infty$ $=1+\frac{2+1}{2}+\frac{4+1}{4}+\frac{6+1}{6}+......to\,\,\infty$ $=1+\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}......to\,\infty ={{e}^{1}}=e$Hence, option [c]is correct.

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