Posted by Jay M. on Sunday, September 17, 2006 at 10:04am.
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
Hi! Very nice site! Thanks you very much! 3HnlKGwMT7
Hello! Good Site! Thanks you! msdwmwidjw
No one has answered this question yet.
Answer this Question
Related Questions
CALC II - Determine the convergence of the following series using the nth-...
Math....Please help I have a deadline for tonight! - Use the geometric sequence ...
Algebra - Use the geometric sequence of numbers 1, 1/3, 1/9, 1/27… to find ...
Geometric series - The sum of the first five terms of a geometric series is 186 ...
Math(arithmetic & Geometric Series) - 1)The sum of 6 terms of an arithmetic...
Geometric Series (Algebra 2) - I need some assistance or a formula when trying ...
Math - Geometric Series - Find the sum of the geometric series 128 - 64 + 32...
calculus - determine whether the series is convergent if so find sum it is the ...
calculus - Another problem: determine whether the series is convergent if so ...
Algebra 2 - Find the sum of the first six terms of the geometric series 81 -27 +...
For Further Reading
