Question Number 476 by 123456 last updated on 11/Jan/15
![given a_n and b_n two real sequence can a serie Σ_(n=1) ^(+∞) a_n and Σ_(n=1) ^(+∞) b_n diverge but Σ_(n=1) ^(+∞) (a_n +b_n ) converge?](https://www.tinkutara.com/question/Q476.png)
$${given}\:{a}_{{n}} \:{and}\:{b}_{{n}} \:{two}\:{real}\:{sequence} \\ $$$${can}\:{a}\:{serie}\:\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}{a}_{{n}} \:{and}\:\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}{b}_{{n}} \:{diverge} \\ $$$${but} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\left({a}_{{n}} +{b}_{{n}} \right)\:{converge}? \\ $$
Commented by prakash jain last updated on 11/Jan/15
![a_n =2^n b_n =−2^n](https://www.tinkutara.com/question/Q478.png)
$${a}_{{n}} =\mathrm{2}^{{n}} \\ $$$${b}_{{n}} =−\mathrm{2}^{{n}} \\ $$