Question

Tìm B (chính xác đến 8 chữ số thập phân ):

\(\dfrac{B}{2}\) = \(\dfrac{1}{1.2.3.4}\) + \(\dfrac{1}{2.3.4.5}\) + \(\dfrac{1}{3.4.5.6}\) + ........ + \(\dfrac{1}{2014.2015.2016}\)

Answer 1

\(\dfrac{B}{2}=\dfrac{1}{1.2.3.4}+\dfrac{1}{2.3.4.5}+...+\dfrac{1}{2014.2015.2016.2017}\)

\(\Leftrightarrow\dfrac{3B}{2}=\dfrac{3}{1.2.3.4}+\dfrac{3}{2.3.4.5}+...+\dfrac{3}{2014.2015.2016.2017}\)

\(=\dfrac{1}{1.2.3}-\dfrac{1}{2.3.4}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{2014.2015.2016}-\dfrac{1}{2015.2016.2017}\)

\(=\dfrac{1}{1.2.3}-\dfrac{1}{2015.2016.2017}\)

Tự làm nốt nhé

Answer 2

Nhân 2 vế cho 3 rồi tách là ra