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, 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
To express the volume of a right circular cylinder as a function of x, we first need to understand the relationship between x, the height, and the radius.
Given that the height (h) is twice the radius (r), we can express this as h = 2r.
Using the volume formula for a right circular cylinder: V = πr^2h, we can substitute h with 2r:
V = πr^2(2r)
V = 2πr^3
Therefore, the volume V of the right circular cylinder can be expressed as a function of x (where x is the radius) as:
V(x) = 2πx^3
This function relates the volume of the cylinder to the radius, which in turn is related to x in this specific scenario.
Please let me know if there's anything else I can help with!