Question

1) 100 x 99 - 99 x 98 + 98 x 97 - 97 x 96 +........+4 x 3 - 3 x 2 + 2 x 1
2) Stim ca a - b + 2(b - c)+ 3(c - 4)=0,aflati a + b + c.

DAU COROANA!!

Answer 1

100 x 99 - 99 x 98 + 98 x 97 - 97 x 96 +........+4 x 3 - 3 x 2 + 2 x 1=
=99(100-98)+97(98-96)+....+3(4-2)+2=
=99×2+97×2+....+3×2+2=
=2×(99+97+...+3+1)=
=2×(100+99+98+97+....+3+2+1-100-98-...-2)=
=2×[(100*101/2-2(50+49+...+1)]=
=2×[(100*101/2-2*50*51/2)]=
=2×(50*101-50*51)=
=2×[50*(101-51)]=
=2×50*50=
=5000

2.
a - b + 2(b - c)+ 3(c - 4)=0
a - b + 2b -2c+ 3c - 12=0
a + b +c - 12=0
a + b +c =12