Mathematics, 09.06.2021 01:30 smorze
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum.
[infinity]
Σ 8/n^2-1
n=3
Answers: 2
![a_3 + a_5 = 4[(\frac{1}{2} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{6})]](/tpl/images/1367/7504/a3ad9.png)
![a_3 + a_5 = 4[(\frac{1}{2} - \frac{1}{6})]](/tpl/images/1367/7504/17ce2.png)
![a_3 + a_5 + a_7= 4[(\frac{1}{2} - \frac{1}{6}) + (\frac{1}{7 - 1} - \frac{1}{7+1})]](/tpl/images/1367/7504/8d295.png)
![a_3 + a_5 + a_7= 4[(\frac{1}{2} - \frac{1}{6}) + (\frac{1}{6} - \frac{1}{8})]](/tpl/images/1367/7504/f2cbf.png)
![a_3 + a_5 + a_7= 4[(\frac{1}{2} - \frac{1}{8})]](/tpl/images/1367/7504/6e045.png)
![a_3 + a_5 + a_7 + ...... + a_{k}= 4[(\frac{1}{2} - \frac{1}{k+1})]](/tpl/images/1367/7504/1a308.png)
![a_4 + a_6 = 4[(\frac{1}{3} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{7})]](/tpl/images/1367/7504/8962f.png)
![a_4 + a_6 = 4[(\frac{1}{3} - \frac{1}{7})]](/tpl/images/1367/7504/c4ede.png)
to both sides![a_4 + a_6 +a_8 = 4[(\frac{1}{3} - \frac{1}{7}) + \frac{1}{7} - \frac{1}{9}]](/tpl/images/1367/7504/3a792.png)
![a_4 + a_6 +a_8 = 4[\frac{1}{3} - \frac{1}{9}]](/tpl/images/1367/7504/ab92d.png)
![a_4 + a_6 + a_8 + ...... + a_{k}= 4[(\frac{1}{3} - \frac{1}{k+1})]](/tpl/images/1367/7504/cd2cc.png)
![S =4[(\frac{1}{2} - \frac{1}{k+1})] + 4[(\frac{1}{3} - \frac{1}{k+1})]](/tpl/images/1367/7504/38ae6.png)
![S =4[(\frac{1}{2}] + 4[(\frac{1}{3}]](/tpl/images/1367/7504/ca14f.png)
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Determine whether the series is convergent or divergent by expressing sn as a telescoping sum.
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