Evaluate the series
-$\sum_{\mathrm{i}=1}^{4} \frac{\mathrm{i}+1}{\mathrm{i}+2}$

A) $\frac{6}{7}$

B) $\frac{21}{10}$

C) $\frac{61}{20}$

D) $\frac{71}{20}$

Question

Evaluate the series
-$\sum_{\mathrm{i}=1}^{4} \frac{\mathrm{i}+1}{\mathrm{i}+2}$

A) $\frac{6}{7}$

B) $\frac{21}{10}$

C) $\frac{61}{20}$

D) $\frac{71}{20}$

Quizplus · Accepted Answer

To evaluate the series $\sum_{\mathrm{i}=1}^{4} \frac{\mathrm{i}+1}{\mathrm{i}+2}$, we substitute the values of $i$ from 1 to 4 into the formula and sum the results:For $i=1$, $\frac{1+1}{1+2} = \frac{2}{3}$For $i=2$, $\frac{2+1}{2+2} = \frac{3}{4}$For $i=3$, $\frac{3+1}{3+2} = \frac{4}{5}$For $i=4$, $\frac{4+1}{4+2} = \frac{5}{6}$Adding these fractions together:$\frac{2}{3} + \frac{3}{4} + \frac{4}{5} + \frac{5}{6} = \frac{8}{12} + \frac{9}{12} + \frac{48}{60} + \frac{50}{60} = \frac{17}{12} + \frac{98}{60} = \frac{85}{60} + \frac{98}{60} = \frac{183}{60} = \frac{61}{20}$Therefore, the sum of the series is $\frac{61}{20}$.

Evaluate the Series - ∑i=14i+1i+2\sum_{\mathrm{i}=1}^{4} \frac{\mathrm{i}+1}{\mathrm{i}+2}∑i=14​i+2i+1​ A) 67\frac{6}{7}76​ B) 2110\frac{21}{10}1021​ C) 6120\frac{61}{20}2061​ D) 7120\frac{71}{20}2071​

Evaluate the Series
- $\sum_{\mathrm{i}=1}^{4} \frac{\mathrm{i}+1}{\mathrm{i}+2}$ A) $\frac{6}{7}$ B) $\frac{21}{10}$ C) $\frac{61}{20}$ D) $\frac{71}{20}$