Certainly! Let's break down the problem step by step.
### Step 1: Calculate the Summation [tex]\(\sum_{2}^{5}\)[/tex]
The notation [tex]\(\sum_{2}^{5}\)[/tex] represents the sum of all integers from 2 to 5, inclusive. So we need to add the numbers 2, 3, 4, and 5 together:
[tex]\[
2 + 3 + 4 + 5
\][/tex]
Let's add these numbers sequentially:
[tex]\[
2 + 3 = 5
\][/tex]
[tex]\[
5 + 4 = 9
\][/tex]
[tex]\[
9 + 5 = 14
\][/tex]
So, the result of the summation [tex]\(\sum_{2}^{5}\)[/tex] is 14.
### Step 2: Calculate the Fraction [tex]\(\frac{1}{5}\)[/tex]
Next, we need to find the value of the fraction [tex]\(\frac{1}{5}\)[/tex]:
[tex]\[
\frac{1}{5} = 0.2
\][/tex]
### Step 3: Combine the Results
Now, we need to add the result of the summation to the fraction:
[tex]\[
14 + 0.2
\][/tex]
Let's perform the addition:
[tex]\[
14 + 0.2 = 14.2
\][/tex]
### Conclusion
Thus, the comprehensive solution to the given problem [tex]\(\sum_{2}^{5} + \frac{1}{5}\)[/tex] is:
[tex]\[
\sum_{2}^{5} = 14
\][/tex]
[tex]\[
\frac{1}{5} = 0.2
\][/tex]
[tex]\[
14 + 0.2 = 14.2
\][/tex]
Therefore, the final answer is [tex]\(14.2\)[/tex].
