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

Question

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

anonymous · Answer

i would try with $\alpha =1$ first

anonymous · Answer

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 $\lim_{n\to \infty}\frac{n}{n+1}=1$

anonymous · Answer

i meant "bounded above by one" not below!

anonymous · Answer

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

anonymous · Answer

then try the general case with $\alpha$

anonymous · Answer

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
$$1/(1+0)=1$$
$$\alpha*1=alpha$$

anonymous · Answer

the last term is alpha

anonymous · Answer

the serries os monotone

anonymous · Answer

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

anonymous · Answer

plz give me medal if i helped