Question

calculați sumele : s1=1×2+2×3+3×4+......+19-20. S2=1×2×3+2×3×4+3×4×5+.......+18×19×20
vă roggggggg!!!!!!!​

Answer 1

S1=1×2+2×3+3×4+...+19×20

S1=1(1+1)+2(2+1)+3(3+1)+…+19(19+1)

S1=1²+1+2²+2+3²+3+….+19²+19

S1=(1²+2²+3²+…..+19²)+(1+2+3+….+19)

S1=19(19+1)(2×19+1)/6 +19×20/2

S1=19×20×39/6+19×10

S1=19×10×13+19×10

S1=190(13+1)

S1=190*14

S1=2660

S2=1×2×3+2×3×4+3×4×5+.......+18×19×20

S2=(2-1)×2×(2+1)+ (3-1)×3×(3+1)+ (4-1)×4×(4+1)+…+ (19-1)×19×(19+1)

S2=(2²-1)×2+(3²-1)×3+(4²-1)×4+…..+(19²-1)×19

S2= 2³-2+3³-3+4³-4+…..+19³-19

S2=(1³+2³+3³+4³+….+19³)-(1+2+3+4+…+19)

  (am adunat și am scăzut 1)

S2=(19×20/2)²-19×20/2

S2=190²-190

S2=190(190-1)

S2=190×189

S2=35 910

Am utilizat formulele:

1+2+3+…+n=n(n+1)/2

1²+2²+3²+….+n²=n(n+1)(2n+1)/6

1³+2³+3³+….+n³=[n(n+1)/2]², sau n²×(n+1)²/4