Question

calculati 6/5*8+6/8*11+6/11*14+...+6/2017*2020 =?

Answer 1

Răspuns

403/1010

Explicație pas cu pas:

Observatii: (acolo aduci la acelasi numitor)

1/5-1/8=3/5*8

1/8-1/11=3/8*11

1/2017-1/2020=3/2017*2020

1/n  - 1/(n+3)=(n+3-n)/n(n+3)=1/n(n+3)

dam 2 factor comun si inlocuim din formula^:

2(3/5*8+3/8*11+3/11*14+...+3/2017*2020 )=2(1/5-1/8+1/8-1/11+....+1/2017-1/2020)

se observa ca se reduc termenii 2 cate 2 inafara de extreme

=2(1/5-1/2020)=2*(404/2020-1/2020)=2*403/2020=403/1010