Giải thích các bước giải:
Bài 2:
a.Chứng minh $\dfrac{2m}{b(b+m)(b+2m)}=\dfrac{1}{b(b+m)}-\dfrac{1}{(b+m)(b+2m)}$
Ta có :
$\begin{split}\dfrac{2m}{b(b+m)(b+2m)}&=\dfrac{b+2m-b}{b(b+m)(b+2m)}\\&=\dfrac{b+2m}{b(b+m)(b+2m)}-\dfrac{b}{b(b+m)(b+2m)}\\&=\dfrac{1}{b(b+m)}-\dfrac{1}{(b+m)(b+2m)}\end{split}$
b.Áp dụng câu a ta có :
$2S=\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+..+\dfrac{2}{37.38.39}$
$\rightarrow 2S=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{37.38}-\dfrac{1}{38.39}$
$\rightarrow 2S=\dfrac{1}{1.2}--\dfrac{1}{38.39}$
$\rightarrow S=\dfrac{1}{2}(\dfrac{1}{2}--\dfrac{1}{38.39})$