Q. 4 - Calculus

Question

Use a sentence to describe what the notation $\sum _{k=2}^{100}\sqrt{k}$ means. (Hint: Start with “The sum of....”)

Step-by-Step Solution

Answer

The sum of square roots of 2 to 100.

Step 1. Given Information:

Given sigma notation: $\sum _{k=2}^{100}\sqrt{k}$

Use a sentence we want to describe what the notation means.

Step 2. Solution:

First we write notation in expand form we get

$\sum _{k=2}^{100}\sqrt{k}=\sqrt{2}+\sqrt{3}+\sqrt{4}+.....+\sqrt{100}$

We observe that given notation represents:

The sum of square roots of 2 to 100.