# PreCalculus

posted by .

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.

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

## Similar Questions

1. ### Algebra

Use the geometric sequence of numbers 1, 1/3, 1/9, 1/27… to find the following: Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms?

Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following: b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms?

4. ### CALC II

Determine the convergence of the following series using the nth-partial sum or geometric series formula. The sum of n=1 to inifitiy 1/(9n^2+3n-2) How do I start?
5. ### Math *URGENT

Please give the answers and solutions for each. 1.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term. 2. Which term if the geometric sequence 18,54,162,486,... is 3,188,646?
6. ### Geometric series

The sum of the first five terms of a geometric series is 186 and the sum of the first six terms is 378. if the fourth term is 48, determine a(first term),r(ratio), t10, S10.
7. ### arithmetic

1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term …
8. ### arithmetic

1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term …
9. ### Math

If S1 = 0.7 and S2 = 2.1 in a geometric series, determine the sum of the first 12 terms in the series. Be sure to show all of your work.
10. ### Pre-Calculus

Q.Determine the sum of each infinite geometric series. t_1= 8 r = -2^1/2 ---------------------------------------- A.This is a divergent series because the absolute value of r is greater than 1. ---------------------------------------- …

More Similar Questions