Câu hỏi của Soái Ca Phước Sơn

Question

tính A = $\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+......+\dfrac{1}{37.38.39}$

Nguyễn Thanh Hằng · Accepted Answer

$A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+.......+\dfrac{1}{37.38.39}$

$=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+.....+\dfrac{1}{37.38}-\dfrac{1}{38.39}$

$=\dfrac{1}{1.2}-\dfrac{1}{38.39}$

$=\dfrac{370}{741}$Câu trả lời: $A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+.......+\dfrac{1}{37.38.39}$

$=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+.....+\dfrac{1}{37.38}-\dfrac{1}{38.39}$

$=\dfrac{1}{1.2}-\dfrac{1}{38.39}$

$=\dfrac{370}{741}$

Đẹp Trai Không Bao Giờ Sai · Answer

$A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+......+\dfrac{1}{37.38.39}$

Ta có:

$\dfrac{1}{1.2.3}=\dfrac{1}{1.2}-\dfrac{1}{2.3}$; $\dfrac{1}{2.3.4}=\dfrac{1}{2.3}-\dfrac{1}{3.4}$;.......

$\Rightarrow A=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...........+\dfrac{1}{37.38}-\dfrac{1}{38.39}$

$\Rightarrow A=\dfrac{1}{1.2}-\dfrac{1}{38.39}$

$=\dfrac{370}{741}$

Vậy $A=\dfrac{370}{741}$Câu trả lời: $A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+......+\dfrac{1}{37.38.39}$

Ta có:

$\dfrac{1}{1.2.3}=\dfrac{1}{1.2}-\dfrac{1}{2.3}$; $\dfrac{1}{2.3.4}=\dfrac{1}{2.3}-\dfrac{1}{3.4}$;.......

$\Rightarrow A=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...........+\dfrac{1}{37.38}-\dfrac{1}{38.39}$

$\Rightarrow A=\dfrac{1}{1.2}-\dfrac{1}{38.39}$

$=\dfrac{370}{741}$

Vậy $A=\dfrac{370}{741}$