Please give the infinite series that makes this famous identity true: e^(pi*i) =-1
Thanks for any help.
The series is:
Sum_(n=0)^99 (pi i)^n/(n!)=-1.000000000000000000+0.×10^-40i
Here, it is evaluated to 100 terms!. As you can see, the real part is -1 and the imaginary part is tending to zero. Here are the first 10 terms of this series as actually written down:
Sum_(n=0)^9 (pi i)^n/(n!) = 1 + ipi-pi^2/2 - (i pi^3)/6 + pi^4/24 + (i pi^5)/120 - pi^6/720 - (i pi^7)/5040 + pi^8/40320 + (i pi^9)/362880.............etc.
