Chapter 5.1, Problem 1E

State whether the given sums are equal or unequal.

1. ${\displaystyle \underset{i=1}{\overset{10}{\sum }}i}$ and ${\displaystyle \underset{k=1}{\overset{10}{\sum }}k}$

${\displaystyle \underset{i=1}{\overset{10}{\sum }}i}$ and ${\displaystyle \underset{i=6}{\overset{15}{\sum }}\left(i-5\right)}$

${\displaystyle \underset{i=1}{\overset{10}{\sum }}i}\left(i-1\right)$ and ${\displaystyle \underset{j=0}{\overset{9}{\sum }}\left(j+1\right)j}$

${\displaystyle \underset{i=1}{\overset{10}{\sum }}i}\left(i-1\right)$ and ${\displaystyle \underset{k=1}{\overset{10}{\sum }}\left(k^2-k\right)}$