Question

Consider the series $\sum_{n=1}^{infinity}[(\frac{1}{(n+8)}-\frac{1}{(n+9)})]$

a. List the nth term, S_n, of the sequence of partial sums for this series.

b. What does the series converge to?

Answer 1

Crivers that linkes - Imags Here Sums fear the ta tan - 1, + n + we know that, Sequence of partial series is Sn = a, +9₂ + Azt – to host an Here are mornires - (nt) a = š ta = šo ay- o -t = 2 Que = int 7) chits) (0+2)(ute) On = conte nts) - (193)(hts) 2, Sn= 15-6)+16 - +*+---+ lots with the who su sa toto + bon momento che sono [ht 8) (utg) (ht7nt)

149) (19) ਉ ਜਾਗ ਆਡ] । ਜੋ ਪੰs ( ਤੇ - *} + ਛ + ਵ + ਨਿ (ੴ - 9) WO (- - 9 ਇੰਚ - - - (+) . [Series converge to 6