Hi
I am find it hard to figure this series out?
Would anyone have any ideas?
1 +2/3+ 8/15 + 48/105 +384/945+ 3840/10395 + 46080/135135 + 645120/2027025 +10321920/34459425+...
Hi
I am find it hard to figure this series out?
Would anyone have any ideas?
1 +2/3+ 8/15 + 48/105 +384/945+ 3840/10395 + 46080/135135 + 645120/2027025 +10321920/34459425+...
Hi hebby,
there is no need to use the sigma format in this case.
Instead.
$\displaystyle a_{n+1}=a_n\left(\frac{2n}{2n+1}\right)$
$\displaystyle \frac{a_{n+1}}{a_n}=\frac{2n}{2n+1}$
As n approaches infinity, the numerator and denominator become indistinguishable, hence the limit of this ratio as n approaches infinity is 1.
The ratio test is inconclusive for this series, it does not tell you if the series converges or diverges.
$\displaystyle \lim_{n\rightarrow\infty}|\frac{a_{n+1}}{a_n}|=\li m_{n\rightarrow\infty}|\frac{T_{n+1}}{T_n}|=1$