Infinite sum wrong result. Bug in Giac?

[danielmewes]

Hi all,

I was reading this bug report for the 50g http://bugs.hpcalc.org/show_bug.cgi?id=238 and entered the same sum into the Prime for testing:

sum from k=1 to infinity (((1+i)/2)^k)

the Prime gives me 0 as the result.

CAS mode, Settings: Exact on, Complex off (turning it on doesn't change the result), Use sqrt on, Use i on.

I can also reproduce this in Giac/Xcas:
`sum(((1+i)/2)^k, k=1...+infinity)`
gives me 0 as well.

In contrast, WolframAlpha says the result is i
http://www.wolframalpha.com/input/?i=sum...o+infinity

Trying a few finite upper boundaries on the Prime suggests that Wolfram Alpha is correct, and Giac/Prime are wrong.

[danielmewes]

Versions:
HP Prime 2014 12 3 (6975)
xcas 1.1.3

[Helge Gabert]

Confirmed.

And, by the same token, sum from k=1 to infinity (((1-i)/2)^k) should return -i, but the Prime also thinks it is zero.

[Edit: Also checked sum from k=1 to infinity (((-1+i)/2)^k) should return -2/5+i/5, but the Prime returns -2/5.

Ditto sum from k=1 to infinity (((-1-i)/2)^k) should return -2/5-i/5, but the Prime returns -2/5 only.]

[parisse]

Fixed in source, thanks.

[danielmewes]

Thanks for the super quick fix Bernard!

Let's see when we get it for the Prime...