$\bullet$ This is taken out of my notes and basically I have to fill in the blanks(1 and 2) but I'm stuck. Can't seem to come up with a general term by even by looking at these patterns. Would appreciate some help here!


A sequence $u_1,u_2,u_3...$ is given by $u_{r+1}=\frac{r+1}{r^2}u_r$ and $u_1=1$. Find an expression for $u_n$ in terms of n.




  1. Therefore, $u_n=$ ....

Alternative method:





  1. Therefore $u_n=$ ....
  • 1
    $\begingroup$ Is it not $\frac{n}{(n-1)!}$ $\endgroup$ Oct 30 '18 at 14:29

$$=\prod_{r=1}^m\dfrac{(n+1-r)}{(n-r)^2}u_{n-m}=u_{n-m}\dfrac n{(n-m)\prod_{r=1}^m(n-r)}$$

Set $m=n-1$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.