探究并计算:1/(2*4)+1/(4*6)+1/(6*8)+…+1/(2010*2012)
问题描述:
探究并计算:1/(2*4)+1/(4*6)+1/(6*8)+…+1/(2010*2012)
答
1/(2*4)+1/(4*6)+1/(6*8)+…+1/(2010*2012)=(1/2)*(1/2-1/4)+(1/2)*(1/4-1/6)+(1/2)*(1/6-1/8)+.+(1/2)*(1/2010-1/2012)=(1/2)*(1/2-1/4+1/4-1/6+1/6-1/8+...1/2010-1/2012)=(1/2)*(1/2-1/2012)=(1/2)*(...