Question

[Megurine Luka]

Tính:

  \(D=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{\left(5n+1\right).\left(5n+6\right)}\)

Tính đầy đủ hộ mik vs. Mik đag cần gấp

Answer 1

[ST]

D = \(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{\left(5n+1\right)\left(5n+6\right)}\)

= \(\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{5n+1}-\frac{1}{5n+6}\right)\)

= \(\frac{1}{5}\left(1-\frac{1}{5n+6}\right)\)

= \(\frac{1}{5}.\frac{5n+5}{5n+6}\)

= \(\frac{n+1}{5n+6}\)