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Further Maths expression for Nth term

The question asks to find an expression for the nth non zero term of the Maclaurin Series for e^3x - e^-3x.

What I tried to do was find the general formula for both parts and add them.

The answer is meant to be 2((3x)^2n-1)/(2n-1)!

Any Help is appreciated, Thanks.
(edited 5 years ago)
Reply 1
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mqb2766
21
Original post by Spleeky
The question asks to find an expression for the nth zero term of the Maclaurin Series for e^3x - e^-3x.

What I tried to do was find the general formula for both parts and add them.

The answer is meant to be 2((3x)^2x-1)/(2x-1)!

Any Help is appreciated, Thanks.


Do you have the expression for the nth term of the Maclaurin series - what did you get for the general formula?
Also, there is no "n" in the answer?
Reply 2
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Spleeky
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8
Original post by mqb2766
Do you have the expression for the nth term of the Maclaurin series - what did you get for the general formula?
Also, there is no "n" in the answer?

Sorry, the answer is meant to be 2((3x)^2n-1)/(2n-1)!.

My working:
(3x)^n/n! - (-3x)^n/n!
(1-(-1)^n)((3x)^n/n!)
Original post by Spleeky
Sorry, the answer is meant to be 2((3x)^2n-1)/(2n-1)!.

My working:
(3x)^n/n! - (-3x)^n/n!
(1-(-1)^n)((3x)^n/n!)

Note that when n is even, your answer is 0. So the kth *non-zero* term will be the result when n = 2k-1
Reply 4
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mqb2766
21
Original post by Spleeky
Sorry, the answer is meant to be 2((3x)^2n-1)/(2n-1)!.

My working:
(3x)^n/n! - (-3x)^n/n!
(1-(-1)^n)((3x)^n/n!)

I guessed what the answer should have been :-)
You've basically done it, you've got the nth term, not the nth zero term. When is the term zero and which value of "n" gives you the right term.
Is it the nth non-zero term you want? The nth zero term is .... 0?
Reply 5
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Spleeky
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8
Original post by DFranklin
Note that when n is even, your answer is 0. So the kth *non-zero* term will be the result when n = 2k-1


Original post by mqb2766
I guessed what the answer should have been :-)
You've basically done it, you've got the nth term, not the nth zero term. When is the term zero and which value of "n" gives you the right term.
Is it the nth non-zero term you want? The nth zero term is .... 0?

Argg, Thanks for that didn't pick up on it saying "non zero".
Reply 6
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mqb2766
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Original post by Spleeky
Argg, Thanks for that didn't pick up on it saying "non zero".


Are you good now?
Reply 7
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Spleeky
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8
Original post by mqb2766
Are you good now?

Yep, thanks for the help.

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