Question

[Nguyễn Thị Thùy Dương]

tính nhanh;A= 3^2/10+3^2/40+3^2/88+...+3^2/340

Answer 1

[Tài Nguyễn Tuấn]

Chào bạn, bạn hãy theo dõi bài giải của mình nhé!

Ta có : 

\(A=\frac{3^2}{10}+\frac{3^2}{40}+\frac{3^2}{88}+...+\frac{3^2}{340}\)

\(=>A=\frac{9}{2\cdot5}+\frac{9}{5\cdot8}+\frac{9}{8\cdot11}+...+\frac{9}{17\cdot20}\)

\(=>A=\frac{9}{3}\left(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+...+\frac{3}{17\cdot20}\right)\)

\(=>A=3\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\right)\)

\(=>A=3\left(\frac{1}{2}-\frac{1}{20}\right)=3\left(\frac{10}{20}-\frac{1}{20}\right)=3\cdot\frac{9}{20}=\frac{27}{20}\)

Chúc bạn học tốt!

Answer 2

[Phạm Tuấn Kiệt]

Chọn mình nhé !  

Ta có:

\(A=\frac{3^2}{10}+\frac{3^2}{40}+\frac{3^2}{88}+...+\frac{3^2}{340}\)

\(\Rightarrow A=3\left(\frac{3}{10}+\frac{3}{40}+\frac{3}{88}+...+\frac{3}{340}\right)\)

\(\Leftrightarrow A=3\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{17.20}\right)\)

\(\Leftrightarrow A=3\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\right)\)

\(\Leftrightarrow A=3\left(\frac{1}{2}-\frac{1}{20}\right)=3.\frac{9}{20}=\frac{27}{20}\)

Vậy \(A=\frac{27}{20}\)