Question

初一新生数学题目.简便计算：1+1/（1+2）+1/（1+2+3）+1/（1+2+3+4）+···+1/（1+2+3+4

Answer 1

等式= 2/(1*2) + 2/(2*3) + 2/(3*4) + .+2/(100*101)

= 2*(1/(1*2)+1/(2*3) + 1/(3*4)+.1/(100*101))

=2*(1-1/2+1/2-1/3+1/3-1/4+.+1/100-1/101)

= 2*(1-1/101)

=200/101