Question

[Nguyễn Huy Trường Lưu]

Có thầy cô hay bạn nào biết kô? Trả lời giúp em

Answer 1

[Nguyễn Huy Trường Lưu]

Có ai không giúp mình với

Answer 2

[Nguyễn Đức Trí]

\(B=\dfrac{5}{3.7}+\dfrac{5}{7.11}+\dfrac{5}{11.15}+...+\dfrac{5}{\left(4n-1\right)\left(4n+3\right)}\)

\(\Rightarrow B=5\left[\dfrac{1}{3.7}+\dfrac{1}{7.11}+\dfrac{1}{11.15}+...+\dfrac{1}{\left(4n-1\right)\left(4n+3\right)}\right]\)

\(\Rightarrow B=5.\dfrac{1}{4}\left[\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+...+\dfrac{1}{4n-1}-\dfrac{1}{4n+3}\right]\)

\(\Rightarrow B=\dfrac{5}{4}\left(\dfrac{1}{3}-\dfrac{1}{4n+3}\right)\)

\(\Rightarrow B=\dfrac{5}{4}\left(\dfrac{4n+3-3}{3\left(4n+3\right)}\right)\)

\(\Rightarrow B=\dfrac{5}{4}\left(\dfrac{4n}{3\left(4n+3\right)}\right)\)

\(\Rightarrow B=\dfrac{5n}{12n+9}\Rightarrow dpcm\)