Chapter E, Problem 41E

Evaluate each telescoping sum.

1. (a) ${\displaystyle \underset{i=1}{\overset{n}{\sum }}[i^4-{(i-1)}^4]}$
2. (b) ${\displaystyle \underset{i=1}{\overset{100}{\sum }}(5^i-5^{i-1})}$
3. (c) ${\displaystyle \underset{i=3}{\overset{99}{\sum }}\left(\frac{1}{i}-\frac{1}{i+1}\right)}$
4. (d) ${\displaystyle \underset{i=1}{\overset{n}{\sum }}(a_i-a_{i-1})}$