r-1 is a factor of r^64 - 1 so use synthetic division (notice the pattern) to divide both sides by r-1 to get
r^63 + r^62 + ... + r + 1 = 2.5(10)^7
the left side is a geometric series with
a = 1
common ratio = r
n = 64
so the sum of the left side = 1(r^64 - 1)/63
then (r^63 - 1)/63 = 2.5(10^7
r^63 = 63(2.5)(10)^7 + 1
taking the 63rd root I got
r = 1.3922
OOOPS, just looked at my solution again and
I'm WRONG!!! (must have had an early morning synapse collapse)
The sum of my series should have said
1(r^64 - 1)/(r-1)
then r^64 - 1 = 2.5(10)^7(r-1)
which brings me back to what we started with.
Sorry, looks like we would have to use some method such as Newtons's Method or some kind of "equation solver" program.
math - I'm having problem trying to solve this question. Solve for x,8 is to 64 ...
math - standard form - please could you check the first 2 then explain the ...
Chemistry - BrO-3 + 5Br- + 6H+ ---> 3Br2 + 3H2O the value of - delta[BrO3]/...
maths - 5x10^2 divide by 7x10^4 what is the answer in standard form
AP Chem - MnS(s) + 2 H+ --> Mn2+ + H2S(g) At 25 C the solubility product ...
chemistry - what is the result of adding (2.5x10^3)+(3.5x10^2) ?
math - Can somebody tell me if this is the right answer. Solve 8 is to 64 as 2 ...
Math - Name the property that justifies each step. [(2x100)+(3x10)]+[(1x100)+(...
Math - How do you solve this equation? 1.5x10^-9=(x^2)/(.858-x)
Calculus - Taylor - could you please help me with solving this problem? #1) Find...