Question

Calculeaza:1+2+3+5+6+...…......+100-23-24-25-26-27-28-29..…..-60=

Answer 1

Sume Gauss.
= 100(1+100)/2 - (23+24+...+60) =
50*101 -(60-23+1)(23+60)/2 =
50*101 -19*83 =
5050 - 1577=
3473.

Answer 2

A=1+2+.........+100
A=100+99+........+1
adunând sumele
2A=101+101+......+101
de 100 de ori
2A=101×100
A=101×50
A=5050
S=1+2+3+.......+60
S=60+59+58+....+1
adunând relațiile
2S=61×60
S=61×30
S=1830
1+2+....+22=22×23/2=11×23=253
-(23+24+....+60)=-(1830-253)=-1577
revenind la cerința
5050-1577=3473