# Sum of (n+1) terms in exponential series

## Homework Statement

S = 1+ x/1! +x2/2! +x3/3! +...+xn/n!
To find S in simple terms.

None

## The Attempt at a Solution

I tried with Taylor's expansion, coshx and sinhx expansions. But cannot see consequence.

fresh_42
Mentor

## Homework Statement

S = 1+ x/1! +x2/2! +x3/3! +...+xn/n!
To find S in simple terms.

None

## The Attempt at a Solution

I tried with Taylor's expansion, coshx and sinhx expansions. But cannot see consequence.
As far as I know, all you can get is ##e^x -\sum_{k=0}^n \frac{x^k}{k!} = r_n(x)## with some boundaries ##c \le r_n(x) \le C##

Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

S = 1+ x/1! +x2/2! +x3/3! +...+xn/n!
To find S in simple terms.

None

## The Attempt at a Solution

I tried with Taylor's expansion, coshx and sinhx expansions. But cannot see consequence.
According to Maple, the sum can be expressed in terms of an incomplete Gamma function ##\Gamma(n+1,x)## and some other factors, but I am not sure you would call that "simple".

Mark44
Mentor
S = 1+ x/1! +x2/2! +x3/3! +...+xn/n!
To find S in simple terms.
Just to check, S isn't given like this, is it?
S = 1+ x/1! +x2/2! +x3/3! +...+xn/n! + ...

Just to check, S isn't given like this, is it?
S = 1+ x/1! +x2/2! +x3/3! +...+xn/n! + ...
No, only n+1 terms.

LCKurtz
Homework Helper
Gold Member

## Homework Statement

S = 1+ x/1! +x2/2! +x3/3! +...+xn/n!
To find S in simple terms.
Those already look like simple terms to me.

coolul007
Gold Member

## Homework Statement

S = 1+ x/1! +x2/2! +x3/3! +...+xn/n!
To find S in simple terms.

None

## The Attempt at a Solution

I tried with Taylor's expansion, coshx and sinhx expansions. But cannot see consequence.
s=ex

Ray Vickson