先观察下列格式.1/1X4=1/3(1-1/4)1/4X7=1/3(1/4-1/7)1/7x10=1/3(1/7-1/10)1/N(N+3)=1/3(1/N-1/N+3)根据规律,计算1/1*4+1/4*7+1/7*10+……+1/2008*2011的值.谢谢

Question

先观察下列格式.1/1X4=1/3(1-1/4) 1/4X7=1/3(1/4-1/7) 1/7x10=1/3(1/7-1/10) 1/N(N+3)=1/3(1/N-1/N+3)
根据规律,计算1/1*4+1/4*7+1/7*10+……+1/2008*2011的值.谢谢

Answer 1

1/(1*4)+1/(4*7)+1/(7*10)+……+1/(2008*2011)
=1/3*(1-1/4)+1/3*(1/4-1/7)+1/3*(1/7-1/10)+...+1/3*(1/2008-1/2011)
=1/3*(1-1/4+1/4-1/7+1/7-1/10+...+1/2008-1/2011)
=1/3*(1-1/2011)
=1/3*2010/2011
=670/2011