I am using the ratio test to determine convergence or convergence of the series defined by ∂ =10; ∂(sub)n+1 = (5/n)∂n

Can someone help?

Question

I am using the ratio test to determine convergence or convergence of the series defined by ∂ =10; ∂(sub)n+1 = (5/n)∂n

Can someone help?

anonymous · Answer

$$
\delta_2= \frac{ 10(5)}1\

\delta_3= \frac{ 10(5^2)}{1*2}\

\delta_4= \frac{ 10(5^3)}{1*2*3}\

$$
Can you write
$$
\delta_n
$$

anonymous · Answer

$$

\delta_n= \frac {10(5^{n-1})}
{(n-1)!}
$$

anonymous · Answer

wow this stuff looks complicated what kind of math is this

anonymous · Answer

$$
\frac {\delta_{n+1}}{\delta_n}=\frac{10\ 5^n}{\frac{\left(10\ 5^{n-1}\right) n!}{(n-1)!}}=\frac{5
   (n-1)!}{n!}=\frac{5}{n}-> 0 < 1

$$
When n goes to Infinity. Series is convergent.

anonymous · Answer

It is Calc II, Calc III stuff