Question

Calculati: 4/1x5 + 4/5x9 + 4/9x13 +....+ 4/2017x2021
DAU 20 DE PUNCTE+COROANA!!!

Answer 1

4/1-4/5+4/5-4/9+........4/2017-4/2021 , se simplifica si ramane
4/1-4/2021  amplifici prima cu 2021 si dupa scazi (asta am avuto si eu la olimpiada)

Answer 2

4/1x5+4/5x9+......+4/2017x2021=
=(5-1)/1x5+ (9-5)/5x9+.........+(2021-2017)/2017x2021
=5/1x5-1/1x5+ 9/5x9- 5/9x5+.......+ 2021/2017x2021- 2017/2017x2021
= 1/4( 1/1x5+ 1/5x9+.........+1/2021x2017)
=1/4*2020/2021
= 505/2021 
Scuze ca am facut cam direct.