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Mumz [18]
3 years ago
7

Determine whether the series is convergent or divergent by expressing Sn as a telescoping sum. If it is convergent, find its sum

. Show all work.
The sum as n goes from 1 to infinity of ln(n/(n+1))
Mathematics
1 answer:
Inessa05 [86]3 years ago
3 0
<span> i'm going to be slightly extra careful in showing each step. specific, ln [n / (n+a million) ]= ln n - ln(n+a million). So, we've sum(n=a million to infinity) ln [n / (n+a million) ] = lim(ok--> infinity) sum(n=a million to ok) ln [n / (n+a million) ] = lim(ok--> infinity) sum(n=a million to ok) [ln n - ln(n+a million)] = lim(ok--> infinity) (ln a million - ln 2) + (ln 2 - ln 3) + ... + (ln ok - ln(ok+a million)) = lim(ok--> infinity) (ln a million - ln(ok+a million)), for the reason that fairly much all the words cancel one yet another. Now, ln a million = 0 and lim(ok--> infinity) ln(ok+a million) is countless. So, the sum diverges to -infinity. IM NOT COMPLETELY SURE

</span>
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