Câu hỏi của Hoàng Như Anh

Question

Tính tổng;$\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}$

Kevin · Accepted Answer

$\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}$$=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{37.38.39}\right)$$=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{37.38}-\frac{1}{38.39}\right)$$=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{38.39}\right)$$=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{1482}\right)$$=\frac{1}{2}.\frac{370}{741}$$=\frac{1}{2}.\frac{370}{741}$$=\frac{185}{741}$  Câu trả lời:  $\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}$$=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{37.38.39}\right)$$=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{37.38}-\frac{1}{38.39}\right)$$=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{38.39}\right)$$=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{1482}\right)$$=\frac{1}{2}.\frac{370}{741}$$=\frac{1}{2}.\frac{370}{741}$$=\frac{185}{741}$

Trang Thị Anh :) · Answer

Đặt    $A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{37.38.39}$$2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{37.38.39}$$2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{37.38}-\frac{1}{38.39}$$2A=\frac{1}{1.2}-\frac{1}{38.39}=\frac{370}{741}$$A=\frac{185}{741}$Chúc bn hc tốt <3Câu trả lời: Đặt    $A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{37.38.39}$$2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{37.38.39}$$2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{37.38}-\frac{1}{38.39}$$2A=\frac{1}{1.2}-\frac{1}{38.39}=\frac{370}{741}$$A=\frac{185}{741}$Chúc bn hc tốt <3

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