**Question 13: Evaluate the Sum**\[ \sum_{i=0}^{3} \frac{1}{i^2 + 1} \]This problem requires evaluating the sum of the series from \( i = 0 \) to \( i = 3 \) for the expression \(\frac{1}{i^2 + 1}\).### Step-by-Step Solution:1. **Substitute \( i = 0 \):**\[ \frac{1}{0^2 + 1} = \frac{1}{1} = 1 \]2. **Substitute \( i = 1 \):**\[ \frac{1}{1^2 + 1} = \frac{1}{2} \]3. **Substitute \( i = 2 \):**\[ \frac{1}{2^2 + 1} = \frac{1}{4 + 1} = \frac{1}{5} \]4. **Substitute \( i = 3 \):**\[ \frac{1}{3^2 + 1} = \frac{1}{9 + 1} = \frac{1}{10} \]### Sum the Evaluated Terms:\[ \sum_{i=0}^{3} \frac{1}{i^2 + 1} = 1 + \frac{1}{2} + \frac{1}{5} + \frac{1}{10} \]### Simplify the Sum:- Convert the fractions to a common denominator of 10 for simplification:\[ 1 = \frac{10}{10} \]\[ \frac{1}{2} = \frac{5}{10} \]\[ \frac{1}{5} = \frac{2}{10} \]\[ \frac{1}{10} = \frac{1}{10} \]- Add the fractions:\[ \frac{10}{10} + \frac{5}{10} + \frac{2}{10} + \frac{1}{10} = \frac{10 + 5 + 2 + 1}{10} = \frac{18}{10} = 1.8 \]### Final Answer:\[ \sum_{i=0}^{3} \frac{1}{i^2 + 1} = 1.8 \]Thus,

Name: **Question 13: Evaluate the Sum**\[ \sum_{i=0}^{3} \frac{1}{i^2 + 1}
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: **Question 13: Evaluate the Sum**\[ \sum_{i=0}^{3} \frac{1}{i^2 + 1} \]This problem requires evaluating the sum of the series from \( i = 0 \) to \( i = 3 \) for the expression \(\frac{1}{i^2 + 1}\).### Step-by-Step Solution:1. **Substitute \( i = 0