Question

[gamoi123]

1/11+1/231+1/651+...+1/11211

Answer 1

[T.Ps]

#)Giải :

Đặt \(A=\frac{1}{11}+\frac{1}{231}+\frac{1}{651}+...+\frac{1}{11211}\)

\(A=\frac{1}{1.11}+\frac{1}{11.21}+\frac{1}{21.31}+...+\frac{1}{101.111}\)

\(A=1-\frac{1}{11}+\frac{1}{11}-\frac{1}{21}+\frac{1}{21}-\frac{1}{31}+...+\frac{1}{101}-\frac{1}{111}\)

\(A=1-\frac{1}{111}\)

\(A=\frac{110}{111}\)

          #~Will~be~Pens~#

Answer 2

[.]

Ta có : \(\frac{1}{11}+\frac{1}{231}+\frac{1}{651}+.....+\frac{1}{11211}\)

• =\(\frac{1}{1.11}+\frac{1}{11.21}+\frac{1}{21.31}+.....+\frac{1}{101.111}\)
• =\(\frac{1}{10}\left(\frac{10}{1.11}+\frac{10}{11.21}+\frac{10}{21.31}+.....+\frac{10}{101.111}\right)\)
• =\(\frac{1}{10}\left(\frac{1}{1}-\frac{1}{11}+\frac{1}{11}-\frac{1}{21}+\frac{1}{21}-\frac{1}{31}+.....+\frac{1}{101}-\frac{1}{111}\right)\)
• =\(\frac{1}{10}\left(1-\frac{1}{111}\right)\)
• =\(\frac{1}{10}.\frac{110}{111}\)
• =\(\frac{11}{111}\)

chúc học tốt !

nhớ nha!