Prob. 14, Chap. 3, in Baby Rudin: The arithmetic mean of a complex sequence
For (c): Consider $s_{2^m} = m, m = 1,2, \dots, s_n = 0$ for all other $n.$ (We don't have $s_n >0$ for all $n,$ but it will give you the idea.)
Prob. 14, Chap. 3, in Baby Rudin: The arithmetic mean of a complex sequence
For (c): Consider $s_{2^m} = m, m = 1,2, \dots, s_n = 0$ for all other $n.$ (We don't have $s_n >0$ for all $n,$ but it will give you the idea.)