Răspuns:
Explicație pas cu pas:
n=2+ 4 +6+ ... + 2018 + 1010
an = a1 + (n - 1)r
a1 = 2; an = 2018; r = 2
2018 = 2 + (n - 1)*2 = 2 + 2n - 2 = 2n
n = 2018 : 2 = 1009 numarul de termeni din suma 2+ 4 +6+ ... + 2018
Sn = n(a1 + an)/2 = 1009(2 + 2018)/2 = 1009*2020/2 = 1009*1010
2+ 4 +6+ ... + 2018 + 1010 = 1009*1010 + 1010 = 1010 (1009 + 1) = 1010*1010 patrat perfect (1010^2)
√1010*1010 = 1010
________________________
1+3+5+ ... +2019
2019 = 1 + (n - 1)*2 = 1 + 2n - 2 = 2n - 1
2n = 2019 + 1 = 2020
n = 2020 : 2 = 1010 termeni in suma
1+3+5+ ... +2019 = 1010 (1 + 2019)/2 = 1010*2020/2 = 1010*1010 = patrat perfect (1010^2)
√1010*1010 = 1010
