Câu hỏi của Nguyễn Tuấn Phong

Question

Tính: 3^2-1/5^2-1.7^2-1/9^2-1.11^2-1/13^2-1...43^2-1/45^2-1 (Dấu / là phân số nhé ^^)

Đoàn Đức Hà · Accepted Answer

$\frac{3^2-1}{5^2-1}\times\frac{7^2-1}{9^2-1}\times\frac{11^2-1}{13^2-1}\times...\times\frac{43^2-1}{45^2-1}$

$=\frac{2\times4}{4\times6}\times\frac{6\times8}{8\times10}\times\frac{10\times12}{12\times14}\times...\times\frac{42\times44}{44\times46}$

$=\frac{2\times4\times6\times8\times...\times42\times44}{4\times6\times8\times10\times...\times44\times46}$

$=\frac{2}{46}=\frac{1}{23}$

Câu trả lời:

$\frac{3^2-1}{5^2-1}\times\frac{7^2-1}{9^2-1}\times\frac{11^2-1}{13^2-1}\times...\times\frac{43^2-1}{45^2-1}$

$=\frac{2\times4}{4\times6}\times\frac{6\times8}{8\times10}\times\frac{10\times12}{12\times14}\times...\times\frac{42\times44}{44\times46}$

$=\frac{2\times4\times6\times8\times...\times42\times44}{4\times6\times8\times10\times...\times44\times46}$

$=\frac{2}{46}=\frac{1}{23}$