Question

Cho mik hỏi bài này thế nào óc sắp nát rồi mà vẫn không nghĩ ra:

1/1x6 + 1/6x11 + 1/11x16 + .... + 1/491x496 + 1/496x501

 

Answer 1

Đặt \(A=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)

\(\Rightarrow5A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{496}+\frac{1}{501}\)

\(\Rightarrow5A=1-\frac{1}{501}=\frac{500}{501}\)

\(\Rightarrow A=\frac{500}{501}:5=\frac{500}{501}.\frac{1}{5}=\frac{100}{501}\)

Answer 2

k mik nhé 

=1/5x(1-1/6+1/6-1/11-1/16+...+1/496-1/501

=1/5x(1-1/501)

=1/5x500/501

=100/501

Answer 3

\(\frac{1}{1\times6}+\frac{1}{6\times11}+\frac{1}{11\times16}+...+\frac{1}{491\times496}+\frac{1}{496\times501}\)

\(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{491}-\frac{1}{496}+\frac{1}{496}-\frac{1}{501}\)

\(=1-\frac{1}{501}\)

\(=\frac{500}{501}\)

P/s tham khảo nha

Answer 4

sorry mình lộn nha

Ghi nhầm

nên dẫn đến đề sai

Answer 5

Đặt: \(A=\frac{1}{1\times6}+\frac{1}{6\times11}+\frac{1}{11\times16}+...+\frac{1}{491\times496}+\frac{1}{496\times501}\)

\(A\times5=\frac{5}{1\times6}+\frac{5}{6\times11}+\frac{5}{11\times16}+...+\frac{1}{491\times496}+\frac{1}{496\times501}\)

\(A\times5=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{491}-\frac{1}{496}+\frac{1}{496}-\frac{1}{501}\)

\(A\times5=1-\frac{1}{501}\)

\(A\times5=\frac{500}{501}\)

\(A=\frac{500}{501}:5\)

\(A=\frac{100}{501}\)

Vậy: \(A=\frac{100}{501}\)

Answer 6

Dm nghĩ lâu quá...haha ra rồi 100/501