Chapter B, Problem 1E

To determine

To write: The sum ${\displaystyle \sum _{i=1}^5\sqrt{i}}$ in expanded form.

Answer to Problem 1E

The sum ${\displaystyle \sum _{i=1}^5\sqrt{i}}$ in expanded form is $\underset{\_}{\sqrt{1}+\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{5}}$.

Explanation of Solution

Definition used:

If $a_m,a_{m+1},\cdots ,a_n$ are real numbers and m and n are integers such that $m\le n$, then ${\displaystyle \sum _{i=m}^n{a}_i}=a_m+a_{m+1}+a_{m+2}+\cdots +a_{n-1}+a_n$.

Calculation:

The given summation is ${\displaystyle \sum _{i=1}^5\sqrt{i}}$.

By using the above mentioned definition, write the sum ${\displaystyle \sum _{i=1}^5\sqrt{i}}$ in expanded form as follows.

${\displaystyle \sum _{i=1}^5\sqrt{i}}=\sqrt{1}+\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{5}$

Therefore, the sum ${\displaystyle \sum _{i=1}^5\sqrt{i}}$ in expanded form is $\underset{\_}{\sqrt{1}+\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{5}}$.