- #1

- 268

- 6

## Homework Statement

S = 1+ x/1! +x

^{2}/2! +x

^{3}/3! +...+x

^{n}/n!

To find S in simple terms.

## Homework Equations

None

## The Attempt at a Solution

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

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- Thread starter ssd
- Start date

- #1

- 268

- 6

S = 1+ x/1! +x

To find S in simple terms.

None

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

- #2

fresh_42

Mentor

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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#### Homework Statement

S = 1+ x/1! +x^{2}/2! +x^{3}/3! +...+x^{n}/n!

To find S in simple terms.

## Homework Equations

None

## The Attempt at a Solution

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

- #3

Ray Vickson

Science Advisor

Homework Helper

Dearly Missed

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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".## Homework Statement

S = 1+ x/1! +x^{2}/2! +x^{3}/3! +...+x^{n}/n!

To find S in simple terms.

## Homework Equations

None

## The Attempt at a Solution

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

- #4

Mark44

Mentor

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Just to check, S isn't given like this, is it?S = 1+ x/1! +x^{2}/2! +x^{3}/3! +...+x^{n}/n!

To find S in simple terms.

S = 1+ x/1! +x

- #5

- 268

- 6

No, only n+1 terms.Just to check, S isn't given like this, is it?

S = 1+ x/1! +x^{2}/2! +x^{3}/3! +...+x^{n}/n!+ ...

- #6

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Those already look like simple terms to me.## Homework Statement

S = 1+ x/1! +x^{2}/2! +x^{3}/3! +...+x^{n}/n!

To find S in simple terms.

- #7

- #8

Ray Vickson

Science Advisor

Homework Helper

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No: absolutely not! The infinite sum is ##e^x## but--at least in the initial post--the OP is asking about the finite sum, just for the first ##n+1## terms of the exponential series.s=e^{x}

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