=4/3.9/8.16/15.25/4096(CÁI NÀY MÌNH BIẾN NÓ VỀ PHÂN SỐ NHA)

=5/512 (BẠN THỰC HIỆN PHÉP TÍNH TỪ TRÁI SANG PHẢI NHÉ)

\(\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.\frac{5^2}{4^6}=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{4096}=\frac{4.9.16.25}{3.8.15.4096}=\frac{3.5}{2.3.256}=\frac{5}{2.256}=\frac{5}{512}\)

# Học tốt.!

=)))

\(\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.....\frac{59^2}{58.60}\)

\(=\frac{2^2.3^2.4^2....59^2}{1.3.2.4.3.5....58.60}\)

\(=\frac{\left(2.3.4...59\right)\left(2.3.4...59\right)}{\left(2.3.4...58\right)\left(3.4.5....60\right)}\)

\(=\frac{59.2}{60}=\frac{59}{30}\)

\(A=\frac{2^2}{1.3}\cdot\frac{2^2}{2.4}\cdot\frac{2^2}{3.5}\cdot\frac{2^2}{4.6}\)

\(A=\frac{4}{3}\cdot\frac{1}{2}\cdot\frac{4}{15}\cdot\frac{1}{6}\)

\(A=\frac{4.1.4.1}{3.2.15.6}\)

\(A=\frac{4}{135}\)

\(\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.\frac{5^2}{4.6}\)

\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.\frac{5.5}{4.6}\)

\(=\frac{2.3.4.5}{1.2.3.4}.\frac{2.3.4.5}{3.4.5.6}\)

\(=\frac{5}{1}.\frac{2}{6}\)

\(=\frac{5}{1}.\frac{1}{3}\)

\(=\frac{5}{3}\)

Đọc kỹ lại đề đi Trần Cao Vỹ Lượng

52/51

\(\text{= 2/1 . 2/3 . 3/2 . 3/4 . 4/3 . 4/5 ....... 50/49.50/51 }\)

Dùng phương pháp khử liên tiếp ta có

\(=\frac{2}{1}-\frac{50}{51}=\frac{52}{51}\)

í nhầm

=200/101 nha bạn

\(\frac{200}{101}\)nha! k nhé

\(A=\frac{1^2}{1.3}+\frac{2^2}{3.5}+...+\frac{1006^2}{2011.2013}\)

\(\Leftrightarrow4A=\frac{2^2.1^2}{2^2-1}+\frac{2^2.2^2}{4^2-1}+...+\frac{2^2.1006^2}{2012^2-1}\)

\(=1006+\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2011.2013}\right)\)

\(=1006+\frac{1}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2011}-\frac{1}{2013}\right)\)

\(=1006+\frac{1}{2}\left(1-\frac{1}{2013}\right)=\frac{2026084}{2013}\)

\(\Rightarrow A=\frac{506521}{2013}\)