1
$\begingroup$

I would like to find the value of

$$\lim_{n\to \infty} \sum_{r=1}^n \frac{r}{1\cdot3\cdot5\cdot7\cdots(2r+1)}.$$

My approach is attached below.

My approach ( click here )

$\endgroup$
4
  • $\begingroup$ math.meta.stackexchange.com/questions/5020/… $\endgroup$
    – evaristegd
    Commented Jul 15, 2019 at 20:44
  • $\begingroup$ Is it mandatory to use MathJax? $\endgroup$
    – Kaushik
    Commented Jul 15, 2019 at 20:47
  • 1
    $\begingroup$ It is much preferred to use MathJax when possible. Images can't be browsed and aren't accessible to those using screen readers, for example. $\endgroup$
    – saulspatz
    Commented Jul 15, 2019 at 21:07
  • $\begingroup$ Oh sorry. I am new to this and i am not used to MathJax. I tried my best and made the question using it. $\endgroup$
    – Kaushik
    Commented Jul 15, 2019 at 21:17

1 Answer 1

Reset to default
6
$\begingroup$

Now note that $\sum_{r=1}^n (T(r-1)-T(r))$ telescopes to $T(0)-T(n)$.

$\endgroup$
3
  • $\begingroup$ Can you please explain how? $\endgroup$
    – Kaushik
    Commented Jul 15, 2019 at 20:51
  • 1
    $\begingroup$ Write out the first several terms and notice the pairs that appear with opposite signs. $\endgroup$
    – RobPratt
    Commented Jul 15, 2019 at 20:53
  • $\begingroup$ Finally I noticed it. Thanks mate! $\endgroup$
    – Kaushik
    Commented Jul 15, 2019 at 21:05

Not the answer you're looking for? Browse other questions tagged .