Question

tính

A =\(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)

Answer 1

A=\(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+....+\frac{1}{990}\) =\(\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{30.33}\)                                                                    =\(\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{33}\right)=\frac{1}{2}.\frac{10}{33}=\frac{5}{33}\)

Answer 2

\(A=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)

\(A=\frac{1}{9}\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)\)

\(A=\frac{1}{9}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)

\(A=\frac{1}{9}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...-\frac{1}{11}\right)\)

\(A=\frac{1}{9}.\frac{10}{11}=\frac{10}{99}\)

Answer 3

sorry nó dài giải ko nổi

Answer 4

A=1/3.(1/3.6+1/6.9+1/9.12+...+1/30.33) A= 1/3.(1/3-1/6+1/6-1/9+1/9-1/12+...+1/30-1/33) A= 1/3.(1/3-1/33) A=1/3.10/33 A=10/99

Answer 5

3A=3/3.6+3/6.9+3/9.12+...+3/30.33

A=1+(-1/6+1/6-1/9+1/9-1/12+...+1/30)-1/33

A=1+0-1/33

A=32/33

Answer 6

3A=3/3.6+3/6.9+3/9.12+...+3/30.33

A=[1+(-1/6+1/6-1/9+1/9-1/12+...+1/30)-1/33]:3

A=32/33:3

A=32/99