Understanding Geometric Sequences with ln

In summary, the conversation is about solving a geometric series using the equation Sn=(u1(rn-1))/(r-1) and simplifying it using ln(a)+ln(b)=ln(a*b). The final answer is ln(x70/y^595) and the conversation ends with a thank you.
  • #1
hostergaard
37
0

Homework Statement



http://img16.imageshack.us/img16/2327/nummer1.jpg

Homework Equations


Sn=(u1(rn-1))/(r-1)

The Attempt at a Solution


I think i need to use the equation for geometric series(above). Or do i use the arithmetic furmula since ln(a/b)=ln(a)-ln(b). I think i am a bit confused...
 
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  • #2
Hint: Simplify the sum using ln(a)+ln(b)=ln(a*b). You will not need the geometric series.
 
  • #3
ohh, i get it. The the answer is ln(x70/y34)
Right?
Thanks for the help! you are great!:wink:
 
  • #4
hostergaard said:
ohh, i get it. The the answer is ln(x70/y34)
Right?
Thanks for the help! you are great!:wink:

Well, in the denominator you should have y*(y^2)*(y^3)*...*(y^34)=y^595. Here I am using the formula 1+2+3+...+n=n(n+1)/2.
Glad I could help. :smile:
 

What is a geometric sequence with ln?

A geometric sequence with ln is a sequence in which each term is obtained by multiplying the previous term by a constant number, and the natural logarithm function (ln) is used to calculate the terms.

How do you find the nth term of a geometric sequence with ln?

To find the nth term of a geometric sequence with ln, use the formula an = a1 * (r)^(n-1), where a1 is the first term of the sequence and r is the common ratio obtained by taking the natural logarithm of the common ratio of the sequence.

What is the common ratio in a geometric sequence with ln?

The common ratio in a geometric sequence with ln is the constant number that is multiplied to each term to obtain the next term. It is obtained by taking the natural logarithm of the common ratio of the sequence.

What is the sum of a finite geometric sequence with ln?

The sum of a finite geometric sequence with ln can be calculated using the formula Sn = a1 * (1 - r^n) / (1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms in the sequence.

What are the applications of geometric sequences with ln?

Geometric sequences with ln are commonly used in financial calculations, such as compound interest and depreciation. They are also used in population growth models and other mathematical and scientific fields.

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