Mathematics, 23.11.2019 03:31 keithlavender123
Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.
[5/1*2]+[5/2*3]+[5/3*4]++[5/n(n+1)] +
Answers: 3
; 5![[\dfrac{5}{1\cdot2}]+[\dfrac{5}{2\cdot3}]+[\dfrac{5}{3\cdot4}]+....+[\dfrac{5}{n\cdot(n+1)}]](/tpl/images/0387/4588/7ac51.png)
![S_n=\sum^{\infty}_{1}\ [\dfrac{5}{n\cdot(n+1)}]=5[\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}]](/tpl/images/0387/4588/bc6b8.png)
![S_n=5\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}=5\sum^{\infty}_{1}[\dfrac{1}{n}-\dfrac{1}{n+1}]](/tpl/images/0387/4588/6ce6d.png)
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Find a formula for the nth partial sum of the series and use it to find the series' sum if the serie...
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