Question

化简（2-√2/1*2）+（3√2-2√3/2*3)+(4√3-3√4/3*4)+...+(100√99-99√100/

Answer 1

（2-√2/1*2）+（3√2-2√3/2*3)+(4√3-3√4/3*4)+...+(100√99-99√100/99*100)

=1-1/2√2+1/2√-1/3√3+1/3√3-1/4√4+.+1/99√99-1/100√100

=1-1/100√100

=1-1/10

=9/10