## graydarl 3 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. satellite73

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

2. satellite73

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. satellite73

i meant "bounded above by one" not below!

4. satellite73

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

5. satellite73

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

6. Fazeelayaz

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. Fazeelayaz

the last term is alpha

8. Fazeelayaz

the serries os monotone

9. Fazeelayaz

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

10. Fazeelayaz

plz give me medal if i helped