Question

Tính tổng S= 1/5.9+1/9.13+1/13.17+1/17.21+1/21.25

Answer 1

\(4S=4.\left(\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{1}{21.25}\right)\)

=\(\frac{4}{5.9}+\frac{4}{9.13}+....+\frac{4}{21.25}_{ }\)

=\(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+....+\frac{1}{21}-\frac{1}{23}\)

=\(\frac{1}{5}-\frac{1}{25}=\frac{5}{25}-\frac{1}{25}=\frac{4}{25}\)

=> \(S=\frac{4}{25}:4=\frac{4}{25}.\frac{1}{4}=\frac{1}{25}\)

Answer 2

\(S=\frac{1}{5\times9}+\frac{1}{9\times13}+...+\frac{1}{21\times25}\)

\(S\times4=\frac{4}{5\times9}=\frac{4}{9\times13}+...+\frac{4}{21\times25}\)

\(S\times4=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{21}-\frac{1}{25}\)

\(S\times4=\frac{1}{5}-\frac{1}{25}\)

\(S\times4=\frac{4}{25}\)

\(S=\frac{1}{25}\)

Answer 3

ta có S=  1/5.9+1/9.13+1/13.17+1/17.21+1/21.25

<=>4S=4.(1/5.9+1/9.13+1/13.17+1/17.21+1/21.25)

<=>4S=4/5.9+4/9.13+4/13.17+4/17.21+4/21.25

<=>4S=1/5-1/9+1/9-1/13+1/13-1/17+1/21-1/25

<=>4S=1/5-1/25

<=>4S=4/25

<=>S=4/25:4

<=>S=1/25

vậy S=1/25

Answer 4

\(S=\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+\frac{1}{17.21}+\frac{1}{21.25}\)

\(4S=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{21}-\frac{1}{25}\)

\(4S=\frac{1}{5}-\frac{1}{25}\)

\(4S=\frac{4}{25}\)

\(\Rightarrow S=\frac{1}{25}\)