Yes, a geometric series is when x < 1, and x^n, where n >1.
so i understand this could be a geometric series, but how would i write out a finite sequence with the one set of terms being a geometric sequence of x^4n
Ok, I've almost got it.
After rearranging i got well, only up to a certain point, don't know how to get it to end since it would seem that the common term would be indefinite.
a(1+x^4+x^8)+bx(1+x^4+x^8)+cx^2(1+x^4+x^8)+dx^3(1+x^4+x^8)
=
(a+bx+cx^2+dx^3)(1+x^4+x^8+...)
but I don't know...
do you mean rearrange the original series or the f(x) function I am solving for? I need to find an f(x) function using just a,b,c,d, and x for the answer.
i'm stumped.
The problem I have is that I have to find a function from the power series:
f(x)=sigma (from n=0 to infinite) (cn)x^n ... where in cn the n is subscript
and then the statement is given cn+4=cn ... where again n+4 and n are subscripts.
then they tell you to suppose a=c0, b=c1, c=c2...
A hemispherical tank of radius 5 feet is situated so that its flat face is on top. It is full of water. Water weighs 62.5 pounds per cubic foot. The work needed to pump the water out of the lip of the tank is ? foot-pounds.
I tried evaluating the integral of pi(125x/3)(5-x)^2 from 0 to 5...
A hemispherical tank of radius 5 feet is situated so that its flat face is on top. It is full of water. Water weighs 62.5 pounds per cubic foot. The work needed to pump the water out of the lip of the tank is ? foot-pounds.
I tried evaluating the integral of pi(125x/3)(5-x)^2 from 0 to 5...