Question

Chứng minh rằng

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

Answer 1

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

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

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

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

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

=>A=\(\frac{1}{80}\)

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

Nên \(\frac{1}{20.23}+\frac{1}{23.26}+\frac{1}{26.29}+....+\frac{1}{77.80}< \frac{1}{9}\)

Answer 2

ko bt

Answer 3

giúp mik nha đng cần gấp

Answer 4

A=\(3 \left(\right. \frac{3}{20.23} + \frac{3}{23.26} + \frac{3}{26.29} + . . . + \frac{3}{77.80} \left.\right)\)

A\(= 3 \left(\right. \frac{1}{20} - \frac{1}{23} + \frac{1}{23} - \frac{1}{26} + \frac{1}{26} - \frac{1}{29} + . . . + \frac{1}{77} - \frac{1}{80} \left.\right)\)

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

A\(= 3 \left(\right. \frac{4}{80} - \frac{1}{80} \left.\right)\)

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

A\(= \frac{9}{80}\)

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

⇒A\(< \frac{1}{9}\)