Question

1) S=4+7+10+..+301
R=1+3+5+..+49

Answer 1

S= (3*1+1) + (3*2+1) + (3*3+1) +....+ (3*100+1)

S=(3*1+3*2+3*3+...+3*100) +(1+1+1+1...+1) (avem 100 de 1)

S=3*(1+2+3+...+100) +100

S=3*100*101/2 + 100

S=3*50*101 +100

S=15015+100

S=15115

R=(2*0+1) + (2*1+1) +...+(2*24+1)

R=2*(0+1+2+3+..+24) + (1+1+1+...+1) (avem 25 de 1)

R=2*24*25/2 +25

R=24*25 + 25

R=625

Sper ca ai inteles. Singura formula pe care am folosit-o e:
$1 + 2 + 3 + .... + n = \frac{n \times (n + 1)}{2}$
(suma lui Gauss)

Answer 2

S  = 4 + 7 + 10 + ....... + 301

→ aflam cati termeni are suma cu ratia 3 ( 7 - 4 = 3;   10 - 7 = 3 )

( 301 - 4 ) : 3 + 1 = 297 : 3 + 1 = 99 + 1 = 100 termeni are suma

→ aplic formula sumei lui Gauss

S = 100 x ( 4 + 301 ) / 2

S = 100 x 305  / 2

S = 50 x 305

S = 15 250

_________________________

R = 1 + 3 + 5 + ........+ 49

→ stabilesc cati termeni are suma cu ratia 2 ( 3 - 1 = 2;    5 - 3 = 2 ...)

( 49 - 1 ) : 2 + 1 = 48 : 2 + 1 = 24 + 1 = 25 termeni are suma

R = 25 x ( 1 + 49 ) / 2

R = 25 x 50  / 2

R  = 25 x 25

R = 625