Question

Vă rog mult astea!!! ​

Answer 1

Folosind formula lui Gauss pentru sume: 1 + 2 + 3 +...+n = n(n+1)/2

a = 2017 + 2 * (1 + 2 + 3 + ... + 2016) = 2017 + 2 * ( 2016 * 2017) / 2 = 2017 + 2016 * 2017 = 2017 * (1 + 2016) = 2017 * 2017

b = 1 + 3 + 5 +...+2017 = 1+2+3+4+5+...2017 - (2+4+6+8+...+2016) = 1+2+3+...+2017 - 2*(1+2+3+4+...+1008) = (2017*(2017+1))/2 - 2*(1008*(1008+1)/2) = (2017*2018)/2 - 2*(1008*1009)/2 = (2017*2018-1008*2018)/2 = 2018*(2017-1008)/2 = 2018*1009/2 = 1009*1009

c = 81 + 2*81 + 3*81 + ... + 49*81 = 81*(1+2+3+...+49) = 81 * (49*(49+1)/2) = 81 * (49*50/2)= 81*49*25=(9^2)*(7^2)*(5^2)=(9*7*5)^2

d = 2*(1+2+3+....+124)+125 = 2*(124*(124+1)/2) + 125 = 2*124*125/2 + 125 = 124*125 + 125 = 125 * (124 + 1) = 125 * 125 = (25*5)*(25*5) = 25*25*25