Posted by ll on Sunday, September 28, 2008 at 9:14pm.
An arithmetic series has a first term of 4 and a common difference of 1. A geometric series has a first term of 8 and a common ratio of 0.5. After how many terms does the sum of the arithmetic series exceed the sum of the geometric series?

math studies  ll, Sunday, September 28, 2008 at 10:13pm
anyone????

math studies  ll, Sunday, September 28, 2008 at 10:30pm
please

math studies  ll, Sunday, September 28, 2008 at 10:31pm
can anyone help?

math studies  Reiny, Sunday, September 28, 2008 at 11:56pm
for the AS
S_{n} = n/2(8 + n1)
= n/2(n9)
for a GS
S_{n} = 8(1.5^n)/(1.5)
so n/2(n9) > 8(1.5^n)/(1.5)
n/2(n9) > 16(1.5^n)
n^2  9n > 32  32(.5^n)
32(.5)^n + n^2  9n  32 > 0
set it equal to zero and attempt to solve it.
This would be a very nasty equation to solve, except you know that n has to be a whole number, so do some trial and error calculations.
eg. n = 2 we get 38 > 0 which is false
if n = 5 we get 44 > 0 which is false
if n = 20 we get 188 > 0 which is true
So somewhere between n=5 and n=20 there should be a solution
(n=12 > 4.0078 > 0 mmmmhhh?)
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