Question

1+三分之一+六分之一+…一千二百七十五分之一

1+1/3+1/6+…+1/1275

Answer 1

1+1/3+1/6+...+1/1275
=1+1/(1+2)+1/(1+2+3)+...+1/(1+2+...+50)
=1+2/2*3+2/3*4+...+2/50*51
=1+2[(1/2-1/3)+(1/3-1/4)+...+(1/50-1/51)]
=1+2(1/2-1/51)
=1+1-2/51
=100/51