Summation

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July 25th 2009, 05:05 AM
usagi_killer

Summation

http://stuff.daniel15.com/cgi-bin/ma...0x%5E%7Bk_i%7D

Find http://stuff.daniel15.com/cgi-bin/ma...i?a_%7B1996%7D.
July 25th 2009, 07:44 AM
red_dog

We have to find the coefficient of $x^{1996}$ in the left member.

The powers of x in the left member are of the form $x^{\displaystyle 3^{k_1}+3^{k_2}+\ldots+3^{k_l}}=x^{3p}$

But 1996 is not divisible to 3. So the coefficient is 0.
July 25th 2009, 08:12 AM
usagi_killer

Thanks what about if http://stuff.daniel15.com/cgi-bin/ma...4....%20%3Ck_m (That sum has http://stuff.daniel15.com/cgi-bin/mathtex.cgi?m terms).

http://stuff.daniel15.com/cgi-bin/ma...20a_3...%20a_m are non-zero.

What would answer be now?
July 26th 2009, 12:59 AM
usagi_killer

Thanks for that, I am not sure how to go about this next part, could anyone please help?

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