Câu hỏi của Nguyễn Ngân Giang

Question

7/2 +19/6+37/12+...+397/132. Mọi người giúp em nhanh nhé ạ, em cần gấp!

Minh Hồng · Accepted Answer

$\dfrac{7}{2}+\dfrac{19}{6}+\dfrac{37}{12}+...+\dfrac{397}{132}\
=\left(3+\dfrac{1}{2}\right)+\left(3+\dfrac{1}{6}\right)+\left(3+\dfrac{1}{12}\right)+...+\left(3+\dfrac{1}{132}\right)$$=\left(3+3+3+...+3\right)+\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{132}\right)$$=\left(3+3+3+...+3\right)+\left(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+...+\dfrac{1}{11\times12}\right)$$=3\times11+\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{11}-\dfrac{1}{12}\right)$$=33+1-\dfrac{1}{12}=\dfrac{407}{12}$Câu trả lời: $\dfrac{7}{2}+\dfrac{19}{6}+\dfrac{37}{12}+...+\dfrac{397}{132}\
=\left(3+\dfrac{1}{2}\right)+\left(3+\dfrac{1}{6}\right)+\left(3+\dfrac{1}{12}\right)+...+\left(3+\dfrac{1}{132}\right)$$=\left(3+3+3+...+3\right)+\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{132}\right)$$=\left(3+3+3+...+3\right)+\left(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+...+\dfrac{1}{11\times12}\right)$$=3\times11+\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{11}-\dfrac{1}{12}\right)$$=33+1-\dfrac{1}{12}=\dfrac{407}{12}$

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