Expert: Sherry Wallin - 2/7/2009

Question
Hi! I'm in a college math class called Fundamentals of
Modern Math- whatever that's suppose to mean, however I
can't figure out this problem.

Find the in each part.
4+4/3+4/9+4/27+4/81...

For the rest of the problems similar to this, I used Gauss'
Trick. Fractions are not my friends. Please help?

Answer
Hi Lu~
    Study the pattern given. The first is 4 or 4/1 or even 4/(3^0). the second number is 4/(3^1). The 3rd number is 4/(3^2), and the fourth number is 4/(3^3) and finally the fifth is 4/(3^4) and the general term is 4/(3^(n-1)). I'm not sure what you mean by 'find the in each part'? (did you mean find the sum?)The bottom line is that this is a geometric series with r = (1/3) or r = 3^-1 so it is the sum(from k=0 to infinity)(4*3^(-k)). Remember that a geometric series is the sum(k=1 to infinity)(ar^(k-1)) = a/(1-r). In your case a = 4 and r = 1/3.