Question

folosind factorul comun claculati 2⁺4⁺6⁺......⁺280 5⁺10⁺15⁺.......⁺5000

Answer 1

1) 2+4+6+...+280=2(1+2+3+...+140)

1+2+3+...+140=140(140+1)/2=140•141/2=70•141=9870

2(1+2+3+...+140)=2•9870=19 740



2) 5+10+15+...+5000=5(1+2+3+...+1000)

1+2+3+...+1000=1000(1000+1)/2=1000•1001/2=500•1001=500 500

5(1+2+3+...+1000)=5•500500=2 502 500

//Am folosit suma Gauss in ambele situatii.
Bafta!