sum (-1)n z2n from
0 to infinity = z7/(1+z2)
i = cos
pi/2+ i sin ppi/2
=exp( i pi/2)(2n+3)i = exp(-(2n+3)pi/2) = e-(2n+3)pi/2
| =| e-(2n+3)pi/2 |
e-pi = 1/epi < 1
Hence the series
e-(2n+3)pi/2 from 2 to infinity
sum (-1)n (e-pi)n from 2 to infinity
sum (-1)n(epi)n from 0 to infinity
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