A series converges if its sequence of partial sums con verges The sum of the

A series converges if its sequence of partial sums

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A series converges if its sequence of partial sums con-verges.The sum of the series is the limit of the sequence ofpartial sums.For example, consider the geometric series defined by the se-quencean=1rn,n=0,1,2,...Then then-th partial sumSnis given bySn=nk=01rk=and, for|r|>1,k=01rk=limn-→Sn=.Thusk=0(2π)k=andk=2(2π)k=.Another situation in which we we can actually compute the par-tial sums occurs if those sums arecollapsing. It may not beobvious that that is the case, but look for it in this example:nk=01k2+9k+20=and thusk=01k2+9k+20=.Correct Answers:(1-(1/r)**(n+1))/(1-(1/r))1/(1-(1/r))2.751938393884111.115318621516531/4-1/(n+5)0.25Generated by c WeBWorK, , Mathematical Association of America2
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