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a) A=1 +1/3+1/5+…..+1/97+1/99/1/1.99+1/3.97+1/5.99+……+1/97.3+1/99.9
b) B=1/2+1/3+1/4+…..+1/99+1/100/99/1+98/2+97/3+……+1/99
2a)CM: 2n/b(b+m)(b+2m)=1/b(b+m)-1/(b+m)(b+2m)
b)Tính tổng:S=1/1.2.3+1/2.3.4+1/3.4.5+….+1/37.38.39
nhanh lên giúp mình với
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 :
$2S=\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+..+\dfrac{2}{37.38.39}$
$\rightarrow 2S=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+…+\dfrac{1}{37.38}-\dfrac{1}{38.39}$
$\rightarrow 2S=\dfrac{1}{1.2}–\dfrac{1}{38.39}$
$\rightarrow S=\dfrac{1}{2}(\dfrac{1}{2}–\dfrac{1}{38.39})$