Question

Simplifică fractia:5+10+15...+100 supra 4+8+12+...80 dau coroana ajutor va rog

Answer 1

(5+10+15+...+100)/(4+8+12+...+80) =

= [5(1+2+3+...+20)]/[4(1+2+3+...+20)] =

= 5/4

La numarator am dat factor comun pe 5, iar la numitor l-am dat factor comun pe 4. Parantezele se simplifica si ramane 5/4.

Answer 2

n[(n+1)/2] suma Gauss

5+10+15+......+100,dam factor comun pe 5

5(1+2+3+....+20)=5(20×21/2)=5×420/2=2100/2=1050

4+8+12+....+80 dam factor comun pe 4

4(1+2+3+...20)=4×(20×21/2)=4×420/2=1680/2=840

(5+10+15+...+100)/(4+8+12+....80)=

5(20×21/2)/4(20×21/2)=

(5×420/2)/(4×420/2)=

(2100/2)/(1680/2)=

1050/840=525/420=5/4