Question

(2+4+6+.........+100)-(1+3+5+........+99)=

Answer 1

S1=2+4+6+......+100
S1=100+......+6+4+2
Adunand membru cu membru
2S1=102+....+102+102+102
S1 are 50 termeni
2S1=102*50
S1=102*50/2=102*25=2550
S2=1+3+5+.......+99
S2=99+....+5+3+1
Adunand membru cu membru
2S2=100+....+100+100+100(50 termeni)
2S2=100*50
S2=100*50/2=100*25=2500
S1-S2=S
S=2550-2500=50
Cum se calculeaza termenii:
(ultimul numar-primul numar):(din cat in cat cresc numerele)+1
(100-2):2+1=98:2+1=49+1=50 termeni
(99-1):2+1=98:2+1=49+1=50 termeni
Sper ca m-am facut inteles