this can be a very good post...

Question

freckles · Answer

the best post ever!

anonymous · Answer

yes, it can, but it isn't

astrophysics · Answer

Seriously though, what's the question it shows it's in calculus 1 so it had me excited :P

idku · Answer

$\Large \displaystyle\sum_{n=k}^{\infty}~f(n)=~?$

(starting from any whole number k)


we know:

$\Large \displaystyle\sum_{n=1}^{\infty}A_n=\frac{A_1}{1-r}$

what is r in initial case?

$\Large \displaystyle r=\lim_{n\rightarrow \infty}\frac{a_{n+1}}{a_n}$

so,

$\Large \displaystyle\sum_{n=k}^{\infty}~f(n)~=~\frac{A_k}{1-r}$


$\Large \displaystyle\sum_{n=k}^{\infty}~f(n)~=\frac{A_k}{\displaystyle1-\left(\lim_{n\rightarrow \infty}\frac{a_{n+1}}{a_n}\right)}$


i don't even know why so many people are viewing....
(btw, just had to depart for a little)

idku · Answer

that is just a general thing that works for any f

idku · Answer

just a quick thought ... ))