Question

\(\frac{1}{11\times16}+\frac{1}{16\times21}+\frac{1}{21\times26}+...+\)\(\frac{1}{61\times66}\)

Answer 1

đặt A= dãy số trên.Ta có:

5A= \(\frac{5}{11x16}+\frac{5}{16x21}+...+\frac{5}{61x66}\)

=> 5A= \(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)

=> 5A = \(\frac{1}{11}-\frac{1}{66}\)

=> 5A= \(\frac{5}{66}\)

=> A=\(\frac{1}{66}\)

Answer 2

\(=\frac{1}{5}\left(\frac{5}{11.16}\frac{5}{16.21}\frac{5}{21.26}+......+\frac{5}{61.66}\right)\)

\(=\frac{1}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+....+\frac{1}{61}+\frac{1}{66}\right)\)

=\(\frac{1}{5}\left(\frac{1}{11}+\frac{1}{66}\right)\)

\(=\frac{1}{5}.\frac{7}{66}\)

\(=\frac{7}{330}\)