Q. 25 - Calculus

Question

Write each of the sums in Exercises 21–28 in sigma notation. Identify $m,n,a_k$ in each problem.  

$5+10+17+26+37+50+65+82+101$

Step-by-Step Solution

Answer

The sigma notation is $\sum _{k=2}^{10}\left(k^2+1\right)$

Step 1. Given Information

The given sum is $5+10+17+26+37+50+65+82+101$

Step 2. Explanation

The sum in sigma notation is written as, 

$$\begin{gathered} 5+10+17+26+37+50+65+82+101=\left(2^2+1\right)+\left(3^2+1\right)+\left(4^2+1\right)+\left(5^2+1\right)+\left(6^2+1\right)+\left(7^2+1\right)+\left(8^2+1\right)+\left(9^2+1\right)+\left({10}^2+1\right) \\ =\sum _{k=2}^{10}\left(k^2+1\right) \\ where, \\ m=2,n=10,a_k=k^2+1 \end{gathered}$$