Question

(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)

Answer 1

(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)

=1+2(1/2-1/3+1/3-1/4+...+1/1000-1/1001)

=1+2(1/2-1/1001)

=2000/1001

(2)1/(1乘4)+1/(4乘7)+...+1/〔(3N-2)乘(3N+1))

=1/3(1-1/4+1/4-1/7+...+1/(3N-2)-1/(3N+1))

=1/3(1-1/(3N+1)

=(1/3)*(3N/(3N+1))

=N/(3N+1)