Answer
a) First Four Terms: $0.9 , 0.09, 0.009, 0.0009$
b) $\lim\limits_{n \to \infty} S_n = 1$
Work Step by Step
$$\sum_{k=1}^{\infty} 9(0.1)^k$$
Part A)
$a_1 = 9(0.1)^1 = 0.9$
$a_2 = 9(0.1)^2 = 0.09$
$a_3 = 9(0.1)^3 = 0.009$
$a_4 = 9(0.1)^4 = 0.0009$
Part B)
$a_1 + a_2 + a_3 + a_4 + ... = 0.9 + 0.09 + 0.009 + 0.0009 + ... = 0.9999...$
The series seems to converge to the value $1$.
