Chứng minh rằng:
a) \(\dfrac{a}{n\left(n+a\right)}\)= \(\dfrac{1}{n}\)- \(\dfrac{1}{n+a}\) ( n, a\(\in\) N sao)
b) Áp dụng câu a tính
A = \(\dfrac{1}{2.3}\)+ \(\dfrac{1}{3.4}\)+.....+ \(\dfrac{1}{99.100}\)
B = \(\dfrac{5}{1.4}\)+ \(\dfrac{5}{4.7}\)+......+ \(\dfrac{5}{100.103}\)
C = \(\dfrac{1}{15}\)+ \(\dfrac{1}{35}\)+....+ \(\dfrac{1}{2499}\)