Consider the series ∑ 𝑛 = 1 ∞ 0.01 . The terms are 𝑎 𝑛 = 0.01 .   a) Find the following partial sums: 𝑆 1 = [ Select ] 1 0.03 0.02 0.01 0 𝑆 2 =   0.02 𝑆 3 = [ Select ] 0.03 4 0.01 0 3 𝑆 4 = [ Select ] 0.4 0.01 0.04 4 1   b) Find the limits:     lim 𝑘 → ∞ 𝑆 𝑘 =   [ Select ] negative infinity 0 infinity 0.01 0.04 and lim 𝑛 → ∞ 𝑎 𝑛 =   [ Select ] 1 infinity 0.01 negative infinity 0   c) Does the series ∑ 𝑛 = 1 ∞ 0.01  converge or diverge? The series diverges   d) Suppose another series ∑ 𝑛 = 1 ∞ 𝑏 𝑛  has some unknown terms 𝑏 𝑛   but we know that lim 𝑛 → ∞ 𝑏 𝑛 = 0.01   (this means the numbers 𝑏 𝑛 are close to 0.01, but not necessarily equal to 0.01.)  What can be said about the convergence of the series ∑ 𝑛 = 1 ∞ 𝑏 𝑛  ? The series diverges