Let f ( x ) = ∫ 0 x t e − t d t . {\displaystyle f(x)=\int _{0}^{x}te^{-t}\;\mathrm {d} t.} Use this function in all parts below.
(b) Given that the following series converges, find the constant c:
S = ∑ n = 0 ∞ ( c − f ( n ) ) . {\displaystyle S=\sum _{n=0}^{\infty }(c-f(n)).}
