Chapter E, Problem 41E

Evaluate each telescoping sum.

(a) ${\displaystyle \underset{i=1}{\overset{n}{\sum }}\left[i^4-{(i-1)}^4\right]}$

(b) ${\displaystyle \underset{i=1}{\overset{100}{\sum }}\left(5^i-5^{i-1}\right)}$

(c) ${\displaystyle \underset{i=3}{\overset{99}{\sum }}\left(\frac{1}{i}-\frac{1}{i+1}\right)}$

(d) ${\displaystyle \underset{i=1}{\overset{n}{\sum }}\left(a_i-a_{i-1}\right)}$