Home page for accesible maths Math 101 Chapter 1: Sequences and Series 1.34 Infinite Series 1.36 Convergence of series

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1.35 Partial sums

For any series we can form the $n^{th}$ partial sum

s_{n}=\sum_{k=1}^{n}a_{k}=a_{1}+a_{2}+\dots+a_{n}

by adding up the first $n$ terms.

Example.

The series $1-1+1-1+1-\dots$ has partial sums $0$ and $1$ . The odd partial sums are $1,1,\dots;$ whereas the even partial sums are $0,0,\dots;$ so the series does not converge.