Question

请问小学六上数学学习实践园地64页题怎么计算：5/(1*2)+5/(2*3)+5/(3*4)+.+5/(48*49)+5

Answer 1

裂项

原式=5*(1-1/2)+5*(1/2-1/3)+5*(1/3-1/4)``````+5*(1/49-1/50)

=5*1-5*1/2+5*1/2-5*1/3+5*1/3-5*1/4+5*1/4``````+5*1/49-5*1/50

=5-5*1/50

=49/10