Let
1 1 1
P = --- + ---- + .....+ ------
1*2 3*4 99*100
1 1 1
Q = ------ + ------ + ....+ ------
51*100 52*99 100*51
Express P/Q in its lowest terms, that is, gcd(P,Q)=1
*** Adapted from a problem appearing at Argentina Mathematical Olympiad in 2014
clc,clearvars
syms p q
p=sym(0); q=sym(0);
for i=1:2:99
p=p+sym(1)/(i*(i+1));
end
for i=51:100
q=q+1/(i*(151-i));
end
r=p/q;
disp([p q r]);
[47979622564155786918478609039662898122617/69720375229712477164533808935312303556800,
317745844795733688201845092977899987567/34860187614856238582266904467656151778400,
151/2]
The first fraction is p, the second is q and the last is p/q, all reduced to lowest terms, so the answer is 151/2.
p =
47979622564155786918478609039662898122617
-----------------------------------------
69720375229712477164533808935312303556800
q =
317745844795733688201845092977899987567
-----------------------------------------
34860187614856238582266904467656151778400
p/q =
151
---
2
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Posted by Charlie
on 2022-03-04 12:55:59 |
... or let the computer do the arithmetic
