## Related questions with answers

Question

Let $\Sigma a_n$ be a convergent series, and let

$R_N=a_{N+1}+a_{N+2}+\cdots \cdot$

be the remainder of the series after the first N terms. Prove that

$\lim _{N \rightarrow \infty} R_N=0 .$

Solution

VerifiedStep 1

1 of 3Let $\sum a_n$ be a convergent series and $R_N = a_{N+1} + a_{N+2} + \cdots$

We want to prove that $\displaystyle \lim_{N \to \infty} R_N = 0$

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