## graydarl Group Title 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 one year ago one year ago

1. satellite73 Group Title

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

2. satellite73 Group Title

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 Group Title

i meant "bounded above by one" not below!

4. satellite73 Group Title

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

5. satellite73 Group Title

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

6. Fazeelayaz Group Title

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 Group Title

the last term is alpha

8. Fazeelayaz Group Title

the serries os monotone

9. Fazeelayaz Group Title

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

10. Fazeelayaz Group Title

plz give me medal if i helped