How can I make these series equal to each other?

[hddd123456789]

Hi,

I'm trying to see if there is an operation or set of operations I can perform on S1 so that it equals S2. I've just been going in circles and it seems I just don't have enough knowledge of how factorials behave in series to crack this. Any hints would be much appreciated.

Hope this makes sense.

Thanks!

 

[mathman]

You can't. The first term of s2 is (-1)! which is infinite.

 

[hddd123456789]

Thanks for the reply; would it help to set k=1 for both series, and deal with the first terms separately? And forgot to mention that S1=e.

 

[mathman]

S1 = (1+a)^b. I suggest you try to understand what this is about.

 

[hddd123456789]

Sorry, you mean understand the problem or the equation in your post? I know that S1 equals (1+a)^b as well as e. But I guess there isn't a similar closed form of S2.

As for the problem, this is just some "fun" exploration of numbers I made up.