Question

Buna seara, am o problema in legatura cu rezolvarea acestei fractii si as aprecia un ajutor :
Simplificati fractia : 1+2+...+80+81/10+11+...+70+71
multumesc

Answer 1

1+2+3+...+80+81=(81x82)/2=3321
10+11+...+70+71=
Intai calculam suma Gauss completa, de la 1 la 71, care este (71x72)/2=2556, apoi scadem 1+2+3+4+5+6+7+8+9=45
2556-45=2511
3321/2511=(3⁴x41)/(3⁴x31)=41/31

Answer 2

1+2+3+.....+80+81=

(81x82)/2=3321
10+11+.....70+71=
(71x72)/2=2556

1+2+3+4+5+6+7+8+9=45
2556-45=2511
3321/2511=(3^4x41)/(3^4x31)=41/31.

................,,,,,,,,,,,,,,,Bafta!