(a) Suppose that Σ∞n=1 an is a convergent series and let m ∈ N with m > 1. Prove that Σ∞n=m an is convergent and that (b) Suppose that m ∈ with m > 1 and that Σ∞n=m an is convergent. If a1, …, am – 1...

(a) Suppose that Σ^∞
_n=1
a_n
is a convergent series and let m ∈ N with m > 1. Prove that Σ^∞
_n=m
a_n
is convergent and that

(b) Suppose that m ∈

with m > 1 and that Σ^∞
_n=m
a_n
is convergent. If a₁, …, a_{m – 1}
are real numbers, prove that 1 ∞ Σn= an is convergent and that Σ^∞
_n=1
a_n
= a₁
+ … + a_{m – 1}
+ Σ^∞
_n=m
a_n