A series {ar} which can be expressed as a sum of differences of successive terms of another series {br}, i.e. that ar=br−br−1so ∑r=anar=bn−b0., as all terms between the first and last cancel out. For example, if ar=1r(r+1)=1r−1r+1,then∑r=1nar=∑r=1n(1r−1r+1)=1−1n+1=nn+1.
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