Question

Calculand S=4+5+6+7...+100,vei obtine
2) Multimea A{x apartine lui Z*|-3≤x-1≤0} numarul de elemente este..

Answer 1

1) nr de termeni: (100-4)+1=97
S=4+5+6+7...+100=
=(4+100)*97:2=104*97:2=52*97=5044

2) daca - 3 ≤ x-1 ≤0 => - 2 ≤ x ≤ 1
=> A∈ {-2,-1,1}
Numarul de elemente a multimii A este 3

Answer 2

S=1+2+3+...+n=n(n+1)/2
S=1+2+3+...+100=100(100+1)/2=50*101=5050
cum in cazul nostru S=4+5+...+100 trebuie scazuta suma 1+2+3=6
deci S=5050-6=5044
2)$-3 \leq x-1 \leq 0$=>$-3+1 \leq x \leq 0+1$
[tex]-2 \leq x \leq 1 [/tex]
A={-2,-1,1}
Deci cardA=3