Suppose { a n } {\displaystyle \{a_{n}\}} is a sequence, and its associated sequence of partial sum s N = ∑ n = 1 N a n {\displaystyle s_{N}=\sum _{n=1}^{N}a_{n}} is given by s N = 3 − N 2 N + 1 {\displaystyle s_{N}=3-{\frac {N}{2N+1}}} . Evaluate lim n → ∞ a n + ∑ n = 1 ∞ a n {\displaystyle \lim _{n\to \infty }a_{n}+\sum _{n=1}^{\infty }a_{n}} .
