Question

C = 4/2.4+4/4.6+4/6.8+ ...... + 4/2008.2010

Answer 1

Gọi A= 4/2.4+4/4.6+4/6.8+...+4/2008.2010 
A/2= 2/2.4+2/4.6+...+2/2008.2010 
Mà 2/2.4=1/2-1/4; 2/4.6=1/4-1/6 .... 
Vậy A/2= (1/2-1/4)+(1/4-1/6)+....+(1/2008-1/2010) 
A/2=1/2-1/2010=2010/4020-2/4020=2008/4... 
A= 2008.2/4020=1004/1005

Answer 2

C = 4/2.4 + 4/4.6 + 4/6.8 + ... + 4/2008.2010

C = 2 . (2/2.4 + 2/4.6 + 2/6.8 + ... + 2/2008.2010)

C = 2 . (1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/2008 - 1/2010)

C = 2 . (1/2 - 1/2010)

C = 2 . 502/1005

C = 1004/1005