Question

calculati a) S=suma S=1+3+5....+90 S=b)3+7+11+15...+43

Answer 1

A

90×(90+1)÷2=
90×91÷2=8190÷2=4095
b
3+7+11+15+19+23+27+31+35+39+43=

Answer 2

a) S=1+3+5....+90  suma primelor numere impare consecutive

1+3+5+.....+2n-1=1+(1+1×2)+(1+2×2)+(1+3×2)+...=1+1+1+.....+2(1+2+3+...+n)=n²

S=1+3+5....89+90=89²+90=7921+90=8011

b) S=3+7+11+15...+43

progresie aritmetica

an=43, a1=3 

an=a1+(n-1)×r

43=3+(n-1)×4

43=3+4n-4

44=4n

n=11

S=[(a1+an)×n]/2=[(1+43)×11]/2=(44×11):2=22×11=242