Chapter B, Problem 41E

(a)

To determine

To evaluate: The telescoping sum ${\displaystyle \sum _{i=1}^n\left[i^4-{\left(i-1\right)}^4\right]}$.

(b)

To determine

To evaluate: The telescoping sum ${\displaystyle \sum _{i=1}^{100}\left[5^i-5^{i-1}\right]}$.

(c)

To determine

To evaluate: The telescoping sum ${\displaystyle \sum _{i=3}^{99}\left(\frac{1}{i}-\frac{1}{i+1}\right)}$.

(d)

To determine

To evaluate: The telescoping sum ${\displaystyle \sum _{i=1}^n\left(a_i-a_{i-1}\right)}$.