Infinite sum wrong result. Bug in Giac?
12-29-2014, 01:55 AM
Post: #1
 danielmewes Junior Member Posts: 29 Joined: Dec 2014
Infinite sum wrong result. Bug in Giac?
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.
12-29-2014, 01:58 AM
Post: #2
 danielmewes Junior Member Posts: 29 Joined: Dec 2014
RE: Infinite sum wrong result. Bug in Giac?
Versions:
HP Prime 2014 12 3 (6975)
xcas 1.1.3
12-29-2014, 02:49 AM (This post was last modified: 12-29-2014 03:40 AM by Helge Gabert.)
Post: #3
 Helge Gabert Senior Member Posts: 467 Joined: Dec 2013
RE: Infinite sum wrong result. Bug in Giac?
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.]
12-29-2014, 09:20 AM
Post: #4
 parisse Senior Member Posts: 1,243 Joined: Dec 2013
RE: Infinite sum wrong result. Bug in Giac?
Fixed in source, thanks.
12-30-2014, 04:07 AM
Post: #5
 danielmewes Junior Member Posts: 29 Joined: Dec 2014
RE: Infinite sum wrong result. Bug in Giac?
Thanks for the super quick fix Bernard!

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