### Home > PC3 > Chapter 3 > Lesson 3.2.2 > Problem3-111

3-111.

What is the difference between the values of each of the following pairs of sigma expressions? Expand each one to find out.

Expand each summation.

1. $\displaystyle \sum _ { j = 3 } ^ { 7 } j ^ { 2 }$ and $\displaystyle \sum _ { k = 3 } ^ { 7 } k ^ { 2 }$

1. $\displaystyle \sum _ { j = 3 } ^ { 7 } j ^ { 2 }$ and $\displaystyle \sum _ { j = 4 } ^ { 8 } ( j - 1 ) ^ { 2 }$