Question

1.Calculați suma :4+5+6+7+.....+100.
2.Calculați x+y,cu x =28+29+..+43 si y=1+2+3+...+27.
Va rog ajutatima la 2 ex repede

Answer 1

1). 4+5+6+7...+100=
n(n+1)/2
n=100-3
n=97
97(97+1)/2=
=97×98/2
Se simplifica 98 cu 2=
97×49=4753

2).
x=28+29+30+...+43
n=43-27
n=16=>
x=16(16+1)/2
Se simplifica 16 cu 2
x=8×17
x=136

y=1+2+3+...27
n=27
27(27+1)/2
27×28/2
Se simplifica 28 cu 2
27×14=378

x+y=136+378
x+y=514

Answer 2

    
[tex]1) \displaystyle \\ Calculam ~numarul~ termenilor: n=100 - 4 + 1 = 96 + 1 = 97 \\ \\ 4+5+6+7+...+100 = \frac{97(100+4)}{2} =\frac{97 \times 104}{2} =97 \times 52 = \boxed{5044} \\ \\ \\ 2) \\ x =28+29+..+43 \\ y=1+2+3+...+27 \\ x+y = y+x = 1+2+3+...+27 + 28+29+..+43 = \\ \\ = \frac{43 (43+1)}{2}= \frac{43 \times 44}{2} = 43 \times 22 = 43*22=\boxed{946}[/tex]