Question

2.a) 333 supra 123-1 supra 123-2 supra 123-.......-20 supra 123
b) 100 supra 150-99 supra 150+98 supra 150-....-3 supra 150+2 supra 150-1 supra 150
Va rog este urgent!

Answer 1

a) 333/123-1/123-2/123-.......-20/123=
= 333/123-(1+2+...+20)/123=
= 333/123-(20×21/2)/123=
= 333/123-210/123=
=123/123=1

b) 100/150-99/150+98/150-....-3/150+2/150-1/150=
nr termeni  100  pe care ii grupam cate 2 
=( 100/150-99/150)+(98/150-97/150)....+(4/150-3/150)+(2/150-1/150)=
=1/150+1/150+....+1/150=50/150=1/3
nr termeni 1/150  ⇒ 100:2=50