Co cai phan nay minh van chua hieu. Mong cac ban lam ho giup nha:
Tinh: A=50-(1/2.1+1/2.3+1/3.4+............+1/50.51)
co ban lam cho minh la: A= 50-(1-1/51)=49+1/51
Minh khong hieu lam ra kieu gi. Cac ban lam ro cho minh nhe
Ta có: $\dfrac{1}{{n\left( {n + 1} \right)}} = \dfrac{1}{n} - \dfrac{1}{{n + 1}}\,\,,\,n \in {N^*}$
Thay n = 1, 2, 3,..., 50 ta được:
$\dfrac{1}{{1.2}} + \dfrac{1}{{2.3}} + ... + \dfrac{1}{{50.51}} = \dfrac{1}{1} - \dfrac{1}{2} + \dfrac{1}{2} - \dfrac{1}{3} + ... + \dfrac{1}{{50}} - \dfrac{1}{{51}} = 1 - \dfrac{1}{{51}}$
Do đó: $A = 50 - \left( {1 - \dfrac{1}{{51}}} \right) = 49 + \dfrac{1}{{51}}$