Question

chứng tỏ: 

A, a/n.(n+a)=1/n-1/n+a

B, dựa vào câu A, tính: 1/15+1/35+...+1/2499

Answer 1

a) 1/n-1/n+a=a/n.(n+a)

=(n+a)-n/n.(n+a)=n-n+a/n.(n+a)

=a/n.(n+a)

b)1/15+1/35+...+1/2499

=1/3.5+1/5.7+......+1/49.51

=1.2/2.3.5+1.2/2.5.7+.....+1.2/2.49.51

=1/2(2/3.5+2/5.7+.....+2/49.51)

=1/2(1/3-1/5+1/5-1/7+.......+1/49-1/50)

=1/2(1/3-1/50)

=1/2(50/150-3/150)

=1/2.47/150

=47/300