PreCalculus
posted by Jay M. .
Determine the sum of the geometric series:
p+p^2+p^3+.....+(n terms)
I know how to work the formulas but I don't understand how I can find 'tn'.
Thanks,
Jay
I'm not sure what you mean by 'tn'. Is that t_n, tsubn?
Let's look at the case where there are a finite number of terms first.
Supppose we have
(1) S=r + r^2 + r^3 + ... + r^n
If we multiply S by r we have
(2)rS=r^2+r^3 + ... + r^(n+1)
If we subtract (2) from (1) we have
(3)SrS=r  r^(n+1)
The left hand side of (3) is S(1r). If we divide both sides by 1r we get
(4) S = (r  r^(n+1))/(1r) This is the formula if we have only n terms.
If we now consider the sum with an infinite number of terms, there's only a slight modification to formula (4).
The left hand side is still S(1r) but the right hand side is simply r, or S(1r)=r so
(5) S=r/(1r) is the sum of an infinite number of terms for the geometric series.
I'm not sure if I answered your question or not, so please repost if I didn't.
the volume V of a right circular cylinder of height h and radius is V=(PIE)r^2h. If the height is twice the radius, express the volume V as a funtion of x
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