Tính S =1/14+1/35+1/65+...+1/350
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\(\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+\frac{1}{104}+\frac{1}{152}=\frac{12}{19}\)
Ai đồng ý với ý kiến của mk thì , mk sẽ tích lại gấp đôi!!!!!!
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Bạn vô câu hỏi tương tự của bạn trần vũ quang anh là: olm.vn/hoi_dap/question/76402.html
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k cho mik nhé
\(\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+\frac{1}{104}+\frac{1}{152}\)
\(=2.\left(\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+\frac{1}{130}+\frac{1}{208}+\frac{1}{304}\right)\)
\(=2.\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+\frac{1}{13.16}+\frac{1}{16.19}\right)\)
\(=2.\frac{1}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{16.19}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{16}-\frac{1}{19}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{19}\right)\)
\(=\frac{2}{3}.\frac{18}{19}=\frac{12}{19}\)
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=1/1.2+1/2.7+1/7.5+1/5.13+1/13.8+1/8.19
=2/1.4+2/4.7+2/7.10+2/10.13+2/13.16+2/16.19(ca tu va mau cung nhan them 2 gia tri khong doi)
=2/3.(3/1.4+3/4.7+3/7.10+3/10.13+3/13.16+3/16.19)
=2/3.(1/1-1/4+1/4-1/7+1/7-1/10+1/101/13+1/13-1/16+1/16-1/19)
=2/3.18/19=12/19
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\(\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+\frac{1}{104}+\frac{1}{152}=\frac{2}{4}+\frac{2}{28}+\frac{2}{70}+\frac{2}{130}+\frac{2}{208}+\frac{2}{304}=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+\frac{2}{13.16}+\frac{2}{16.19}\)rồi phần còn lại em tự tính nhé
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1/2 + 1/14 + 1/35 + 1/65 + 1/104 + 1/152 = 12/19 nhé bạn !
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`Answer:`
\(S=\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+...+\frac{1}{350}\)
\(\Rightarrow S=\frac{2}{28}+\frac{2}{70}+\frac{2}{130}+...+\frac{2}{700}\)
\(\Rightarrow S=\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+...+\frac{2}{25.28}\)
\(\Rightarrow S=\frac{2}{3}\left(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{25.28}\right)\)
\(\Rightarrow S=\frac{2}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(\Rightarrow S=\frac{2}{3}.\frac{3}{14}\)
\(\Rightarrow S=\frac{1}{7}\)