# Quick Maclarin expansion question...Watch

#1
How do I go about showing why e^x/(1+e^x) will have no even powers of x... I've done some expansion but I'm not sure how to show it will always be the case....
0
8 years ago
#2
I'd start by finding and showing that, when evaluated at , it is equal to zero when is even (and greater than 0). You can find the general expression for by differentiating a few times to spot a pattern and proving it's true by induction.

EDIT: Actually, here's a better way.

The constant term in the Maclaurin series is , so consider the function . The Maclaurin series of this function has only odd powers of x if and only if it is an odd function, so if you can show that then you're done. [You can get your original function back by adding to both sides.]
1
#3
(Original post by nuodai)
I'd start by finding and showing that, when evaluated at , it is equal to zero when is even (and greater than 0). You can find the general expression for by differentiating a few times to spot a pattern and proving it's true by induction.

EDIT: Actually, here's a better way.

The constant term in the Maclaurin series is , so consider the function . The Maclaurin series of this function has only odd powers of x if and only if it is an odd function, so if you can show that then you're done. [You can get your original function back by adding to both sides.]
Ahh Thanks soooo much!!!
0
X

new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• Cardiff Metropolitan University
Sat, 27 Apr '19
• University of East Anglia
Could you inspire the next generation? Find out more about becoming a Primary teacher with UEA… Postgraduate
Sat, 27 Apr '19
• Anglia Ruskin University
Health, Education, Medicine and Social Care; Arts, Humanities and Social Sciences; Business and Law; Science and Engineering Undergraduate
Sat, 27 Apr '19

### Poll

Join the discussion

#### Have you registered to vote?

Yes! (564)
37.65%
No - but I will (117)
7.81%
No - I don't want to (108)
7.21%
No - I can't vote (<18, not in UK, etc) (709)
47.33%