Sum of (n+1) terms in exponential series

  • Thread starter ssd
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  • #1
ssd
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Homework Statement



S = 1+ x/1! +x2/2! +x3/3! +...+xn/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.
 

Answers and Replies

  • #2
14,879
12,407

Homework Statement



S = 1+ x/1! +x2/2! +x3/3! +...+xn/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.
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##
 
  • #3
Ray Vickson
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Homework Statement



S = 1+ x/1! +x2/2! +x3/3! +...+xn/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.
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".
 
  • #4
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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! + ...
 
  • #5
ssd
268
6
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.
 
  • #6
LCKurtz
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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. :oldsmile:
 
  • #7
coolul007
Gold Member
267
8

Homework Statement



S = 1+ x/1! +x2/2! +x3/3! +...+xn/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.
s=ex
 
  • #8
Ray Vickson
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s=ex
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.
 

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