Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

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?

$${given}\:{a}_{{n}} \:{and}\:{b}_{{n}} \:{two}\:{real}\:{sequence} \\ $$$${can}\:{a}\:{serie}\:\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}{a}_{{n}} \:{and}\:\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}{b}_{{n}} \:{diverge} \\ $$$${but} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\left({a}_{{n}} +{b}_{{n}} \right)\:{converge}? \\ $$

Commented by prakash jain last updated on 11/Jan/15

a_n =2^n   b_n =−2^n

$${a}_{{n}} =\mathrm{2}^{{n}} \\ $$$${b}_{{n}} =−\mathrm{2}^{{n}} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com