Question

计算：三分之一+十五分之一+三十五分之一+……+九千九百九十九分之一=?

Answer 1

1/3+1/15+1/35……+1/9999

=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+……+1/2(1/99-1/101)

=1/2(1-1/3+1/3-1/5+1/5-1/7+……+1/99-1/101)

=50/101