Question

a)tinh nhanh

b) CMR A chia het cho 9

A=9/2 + 9/6 + 9/12 + 9/20 + ... + 9/3080

3 like nha !!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

\(A=\frac{9}{2}+\frac{9}{6}+\frac{9}{12}+....+\frac{9}{3080}\)

\(A=9.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{3080}\right)\)chia hết cho 9 (Đpcm)

\(A=9.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{55.56}\right)\)

\(A=9.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{55}-\frac{1}{56}\right)\)

\(A=9.\left(1-\frac{1}{56}\right)=9.\frac{55}{56}\)

\(A=\frac{495}{56}\)