Caldus
Apr20-04, 09:52 PM
I get a number that is too big when I calculate the coefficient of x^25 in:
(2x - (3/x^2))^58
This is how I found the coefficient:
Note that (58) = A combination value...
k
(58) * (2x)^(58-k) * (-3/x^2)^k
k
(58) * (2)^(58 - k) * (x)^(58 - k) * (-3)^k * (1/x^2)^k
k
(58) * (2)^(58 - k) * (-3)^k * (x)^(58 - k) * (x)^-2k
k
(58) * (2)^(58 - k) * (-3)^k * (x)^(58 - 3k)
k
58 - 3k = 25
-3k = -33
k = 11
So:
(58) * 2^47 * (-3)^11 * (x)^25
11
This comes out to be a gigantic number. So I am unsure whether it is anywhere close to being correct despite that I thought that I followed the steps correctly. : \
(2x - (3/x^2))^58
This is how I found the coefficient:
Note that (58) = A combination value...
k
(58) * (2x)^(58-k) * (-3/x^2)^k
k
(58) * (2)^(58 - k) * (x)^(58 - k) * (-3)^k * (1/x^2)^k
k
(58) * (2)^(58 - k) * (-3)^k * (x)^(58 - k) * (x)^-2k
k
(58) * (2)^(58 - k) * (-3)^k * (x)^(58 - 3k)
k
58 - 3k = 25
-3k = -33
k = 11
So:
(58) * 2^47 * (-3)^11 * (x)^25
11
This comes out to be a gigantic number. So I am unsure whether it is anywhere close to being correct despite that I thought that I followed the steps correctly. : \