Tính hợp lí
B=5/6+5/66+5/176+5/336+5/546+5/806
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\(\frac{5}{6}+\frac{5}{66}+\frac{5}{176}+\frac{5}{336}\)
\(=5\left(\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+\frac{1}{336}\right)\)
\(=5\left(\frac{4}{21}\right)\)
\(=\frac{20}{21}\)
mình thấy nó dễ như toán lớp 4 (dạng bài tập của p/s Ai Cập) . câu trả lời của mik như sau :
5/6 + 5/66 + 5/176 + 5/ 336
= 5/1x6 + 5/6x11 +5/11x16 + 5/16x21
= 6-1/1x6 + 11-6/6x11 + 16-11/11x16 +21-16/16x21
tách ra rồi rút gọn còn
=1- 1/6+1/6-1/11+1/11- 1/16+1/16-1/21
=1- 1/21 = 20/21
\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)
\(B=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{92.95}\)
\(=\frac{5-2}{2.5}+\frac{8-5}{5.8}+\frac{11-8}{8.11}+...+\frac{92-92}{92.95}\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{92}-\frac{1}{95}\)
\(=\frac{1}{2}-\frac{1}{95}=\frac{93}{190}\)
\(C=\frac{5}{6}+\frac{5}{66}+\frac{5}{176}+\frac{5}{336}\)
\(=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}\)
\(=\frac{6-1}{1.6}+\frac{11-6}{6.11}+\frac{16-11}{11.16}+\frac{21-16}{16.21}\)
\(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}\)
\(=1-\frac{1}{21}=\frac{20}{21}\)
[ HỌC TỐT]
\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)
\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=\frac{1}{2}-\frac{1}{100}\)
\(A=\frac{100}{200}-\frac{2}{200}\)
\(A=\frac{98}{200}=\frac{49}{100}\)
\(D=\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+\frac{1}{336}+\frac{1}{546}\)
\(D=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}\)
\(D=\frac{1}{5}\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}\right)\)
\(D=\frac{1}{5}\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{21}-\frac{1}{26}\right)\)
\(D=\frac{1}{5}\left(\frac{1}{1}-\frac{1}{26}\right)\)
\(D=\frac{1}{5}.\frac{25}{26}=\frac{5}{26}\)
\(9+2+5+3+7+8+4+2+9+6+4+65+6+7+4+6+3+7+4+8+5+9+08+87+1+2+3+4+2+3+2+5+6+767+5+75+6+4+6+5+66+5+7+546+46+43+6+3+6+4+6+7+8878+68+68+6+7+9+9=10961\)
20/21