Question

[Nguyễn Phương Linh]

 

Nhanh lên mình cần gấp! 

4	+	4	+ … +	4	=
7 x 8		8 x 9		76 x 77

Answer 1

[Đoàn Đức Hà]

\(\frac{4}{7\times8}+\frac{4}{8\times9}+...+\frac{4}{76\times77}\)

\(=4\times\left(\frac{1}{7\times8}+\frac{1}{8\times9}+...+\frac{1}{76\times77}\right)\)

\(=4\times\left(\frac{8-7}{7\times8}+\frac{9-8}{8\times9}+...+\frac{77-76}{76\times77}\right)\)

\(=4\times\left(\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{76}-\frac{1}{77}\right)\)

\(=4\times\left(\frac{1}{7}-\frac{1}{77}\right)\)

\(=\frac{40}{77}\)