Question

Chứng minh rằng \(\frac{1}{20.23}\)+\(\frac{1}{23.26}\)+\(\frac{1}{26.29}\)+.....+\(\frac{1}{77.80}\)<\(\frac{1}{9}\)

Trả lời chi tiết nhé >< cảm ơn mọi người

Answer 1

\(\frac{1}{20.23}+\frac{1}{23.26}+...+\frac{1}{77.80}\)

\(=\frac{1}{3}.\left(\frac{3}{20.23}+\frac{3}{23.26}+...+\frac{3}{27.80}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+...+\frac{1}{77}-\frac{1}{80}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{20}-\frac{1}{80}\right)\)

\(=\frac{1}{3}.\frac{3}{80}\)

\(=\frac{1}{80}< \frac{1}{9}\)

Answer 2

oh oh oh oh

Answer 3

Bạn ơi cách này dễ hiểu hơn nè:

Đặt X =\(\frac{1}{20.23}\)+\(\frac{1}{23.26}\)+..................+\(\frac{1}{77.80}\).Ta có:

3.X= 3.(\(\frac{1}{20.23}\)+\(\frac{1}{23.26}\)+................+\(\frac{1}{77.80}\))

3.X=3.\(\frac{1}{20.23}\)+3.\(\frac{1}{23.26}\)+......................+3.\(\frac{1}{77.80}\)

3.X=\(\frac{3}{20.23}\)+\(\frac{3}{23.26}\)+............................+\(\frac{3}{77.80}\)

3.X=\(\frac{1}{20}\)-\(\frac{1}{23}\)+\(\frac{1}{23}\)-\(\frac{1}{26}\)+...................+\(\frac{1}{77}\)-\(\frac{1}{80}\)

3.X=\(\frac{1}{20}\)-\(\frac{1}{80}\)

3.X=\(\frac{3}{80}\)

X=\(\frac{3}{80}\):3

X=\(\frac{3}{80}\).\(\frac{1}{3}\)

X=\(\frac{1}{80}\)<\(\frac{1}{9}\)

Chúc bạn học tốt!