- #1
Maatttt0
- 37
- 0
Homework Statement
This isn't the whole question, I understand the prior parts but somehow stuck on the "easy" part :( Need to solve a geometric progession problem.. find the sum of:
h(1 + 3^h + 3^2h + ... + 3^(n-1)h)
Where nh = 1
The sum should equal to (2h)/((3^h) -1) which is given as is a prove question
Homework Equations
N/A
The Attempt at a Solution
h(1 + 3^h + 3^2h + ... + 3^(n-1)h) --- this is the list
(h(1-(3^h)^(n-1)))/(1-3^h) --- using the formula Sn = a(1-r^n)/(1-r)
simplify slightly (using nh = 1)
= (h(1-3^(1-h)))/(1-3^h)
times top and bottom by -1 to match the denominator of answer
= (h(3^(1-h) - 1))/((3^h) -1)
and now I can't seem to get the final answer out.
Hopefully I've included enough info for you guys to understand what I'm going on about lol - and apologise for the excess of brackets :S
Thank you in advance :D