posted by Jay M. on .
Determine the sum of the geometric series:
I know how to work the formulas but I don't understand how I can find 'tn'.
I'm not sure what you mean by 'tn'. Is that t_n, t-sub-n?
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)S-rS=r - r^(n+1)
The left hand side of (3) is S(1-r). If we divide both sides by 1-r we get
(4) S = (r - r^(n+1))/(1-r) 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(1-r) but the right hand side is simply r, or S(1-r)=r so
(5) S=r/(1-r) 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