Infinite Geometric Series type question

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November 3rd 2009, 12:14 PM
ItallionStallion

Infinite Geometric Series type question

I know how to determine the sum of a geometric sequence. But I had missed school and this question kinda throws me off balance a bit.

An oil well produces 25 000 barrels of oil during its first month of production. Suppose its production drops by 5% each month.

A) estimate the total production before the well runs dry.

B) explain how you estimated the total production in part a, identify any assumptions you have made. Explain how the assumptions affect the estimate.
November 3rd 2009, 01:39 PM
CaptainBlack

Quote:

Originally Posted by ItallionStallion

I know how to determine the sum of a geometric sequence. But I had missed school and this question kinda throws me off balance a bit.

An oil well produces 25 000 barrels of oil during its first month of production. Suppose its production drops by 5% each month.

A) estimate the total production before the well runs dry.

B) explain how you estimated the total production in part a, identify any assumptions you have made. Explain how the assumptions affect the estimate.

Total production:

$p=25000 (1+0.95+0.95^2+\ ..\ +0.95^n+\ ...) \ \ \ \ ...(1)$

Now observe that :

$(1-x)(1+x+x^2+...+x^n) = (1+x+x^2+...+x^n)-(x+x^2+...+x^{n+1})=1-x^{n+1}$

so use this to estimate the sum in $(1)$

CB
November 3rd 2009, 02:27 PM
ItallionStallion

Quote:

Originally Posted by CaptainBlack

Total production:

$p=25000 (1+0.95+0.95^2+\ ..\ +0.95^n+\ ...) \ \ \ \ ...(1)$

Now observe that :

$(1-x)(1+x+x^2+...+x^n) = (1+x+x^2+...+x^n)-(x+x^2+...+x^{n+1})=1-x^{n+1}$

so use this to estimate the sum in $(1)$

CB

I don't understand this completely. I've been home sick and had gotten my homework and I only figured out how to find the sum xD.