Find if the series converges or diverges...

Question

anonymous · Answer

$$1-\frac{1*3}{3!}+\frac{1*3*5}{5!}-\frac{1*3*5*7}{7!}..+...$$

anonymous · Answer

I know that it alternates between - and + so its probably (-1)^n(some formula)/(some formula)!

anonymous · Answer

the bottom pattern is like 

1!,3!,5!,7!,

so the fomula is probably something like --->even integer -1

anonymous · Answer

But Im confused about how I can get the top pattern formula

anonymous · Answer

you know what the top is also probably some--> even integer -1 but 

how does it keep adding on to the last multiple like that?

anonymous · Answer

anonymous · Answer

but what about the top term?

ganeshie8 · Answer

ive deleted as i saw a mistake in it lol, try to simplify the terms first...

ganeshie8 · Answer

$\large \frac{(-1)^{n+1}}{2^{n-1}(n-1)!}$

ganeshie8 · Answer

see if this works

anonymous · Answer

I got it! its (2n-1)! at the bottom and probably the same thing at the top but how does the previous multiplier stay the same?

ganeshie8 · Answer

i feel top is not that easy to get...  

could u check if the nth term i gave earlier works ?

ganeshie8 · Answer

$\large a_n =  \frac{(-1)^{n+1}}{2^{n-1}(n-1)!}$

ganeshie8 · Answer

$\large a_1 = 1  $

$\large a_2 = -\frac{1}{2}  $

$\large a_3 = \frac{1}{2^2(2!)}  $

ganeshie8 · Answer

ganeshie8 · Answer

hey let me knw if smthng doesnt make sense..