Evaluate P/Q, given:

P= 1-2^-2+4^-2-5^-2+7 ^-2-8^-2+10^-2 -11^-2+13^-2-14^-2+...

Q= 1+2^-2-4^-2-5^-2+7 ^-2+8^-2-10^-2 -11^-2+13^-2+14^-2+...

((1/(6n+1)^2-1/(6n+2)^2+1/(6n+4)^2-1/(6n+5)^2)/((1/(6n+1)^2+1/(6n+2)^2-1/(6n+4)^2-1/(6n+5)^2))) is worth 1/3 in the limit, according to wolframalpha.

On reflection, possibly a bit unfair to wolframalpha. The exact expression is:

(sum n=0 to infinity ((1/(6n+1)^2-1/(6n+2)^2+1/(6n+4)^2-1/(6n+5)^2))/(sum n=0 to infinity (1/(6n+1)^2+1/(6n+2)^2-1/(6n+4)^2-1/(6n+5)^2))), [for the precise wolframalpha syntax required see comment 4]

so the original version was open to misinterpretation.

 

 

Edited on October 13, 2012, 10:24 am

Posted by broll on 2012-10-12 10:31:35