## anonymous 4 years ago Can someone hlep me with this math problem? serie : an=(alpha*n)/(n+1), n>=1 (alpha is from R-real number). I must determine if the series is monotone and bouded thank you very much

1. anonymous

i would try with $$\alpha =1$$ first

2. anonymous

in this case you would get $$a_n=\frac{n}{n+1}$$ which is bounded below by $$1$$ since $$\frac{n}{n+1}<1$$ for all $$n$$ and $$\lim_{n\to \infty}\frac{n}{n+1}=1$$

3. anonymous

i meant "bounded above by one" not below!

4. anonymous

it is monotone increasing as you can check by taking the derivative and seeing that is always positive

5. anonymous

then try the general case with $$\alpha$$

6. anonymous

yes alpha* n/(n+1) limi$\lim_{x \rightarrow \infty}{n/n+1}$ $n/n(1+1/n)=1/(1+1/n)$ take limit to infinity $1/(1+0)=1$ $\alpha*1=alpha$

7. anonymous

the last term is alpha

8. anonymous

the serries os monotone

9. anonymous

the serries is also bounded below becaise it says n>1 soo first term is 1

10. anonymous

plz give me medal if i helped