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3S= 3/2.5+3/5.8+....+3/17.20
= (5-2)/2.5+(8-5)/5.8+....+(20-17)/17.20
= 1/2 - 1/5 + 1/5 - 1/8 + ...... + 1/17 - 1/20 = 1/2 - 1/20 = 9/20
=> S = 3/20
\(S=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{17.20}\)
\(S=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\right)\)
\(S=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{20}\right)\)
\(S=\frac{1}{3}.\frac{9}{20}\)
\(S=\frac{3}{20}\)
\(S=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{17.20}\)
\(S=3.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\right)\)
\(S=3.\left(\frac{1}{2}-\frac{1}{20}\right)\)
\(S=3.\frac{9}{20}=\frac{27}{20}\)
\(a.\frac{2}{3}+\frac{5}{7}=\frac{14}{21}+\frac{15}{21}=\frac{19}{21}\)
\(b.\frac{3}{2}.\frac{4}{5}-\frac{1}{35}=\frac{6}{5}-\frac{1}{35}=\frac{42}{35}-\frac{1}{35}=\frac{41}{35}\)
\(c.\left(\frac{20}{3}-\frac{22}{5}\right):\frac{1}{15}=\left(\frac{100}{15}-\frac{66}{15}\right):\frac{1}{15}=\frac{34}{15}:\frac{1}{15}=\frac{34}{15}x15=34\)
a) \(\frac{2}{3}+\frac{5}{7}=\frac{14}{21}+\frac{15}{21}=\frac{14+15}{21}=\frac{29}{21}\)
b)\(\frac{3}{2}.\frac{4}{5}-\frac{13}{5}=\frac{3.4}{2.5}-\frac{13}{5}=\frac{12}{10}-\frac{13}{5}=\frac{6}{5}-\frac{13}{5}=-\frac{7}{5}\)
c)\(\left(\frac{20}{3}-\frac{22}{5}\right):\frac{1}{15}=\left(\frac{100}{15}-\frac{66}{15}\right):\frac{1}{15}=\frac{44}{15}.15=44\)
\(a.x+9=2\frac{1}{3}\)
\(x=2\frac{1}{3}-9\)
\(x=-\frac{20}{3}\)
\(b.\frac{-5}{2}.x=\frac{1}{10}\)
\(x=\frac{1}{10}:\frac{-5}{2}\)
\(x=-\frac{1}{25}\)
a)
<=> x=\(\frac{7}{3}-9=-\frac{20}{3}\)
b)
<=> x=\(\frac{1}{10}:\frac{-5}{2}=-\frac{2}{25}\)
Chứng minh A < 2.
hu hu hu............................................... giup mình với
\(A< \frac{1}{1}+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(A< 1+\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{50}\)
\(A< 2-\frac{1}{50}< 2\)
Vậy A < 2
\(A=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+.....+\frac{1}{50^2}\)
\(A=\frac{1}{1^2}+\frac{1}{2\times2}+\frac{1}{3\times3}+\frac{1}{4\times4}+.....+\frac{1}{50\times50}\)
\(A< \frac{1}{1}+\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+.....+\frac{1}{49\times50}\)
\(A< 1+\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{49}-\frac{1}{50}\)
\(A< 2-\frac{1}{50}\)
\(2-\frac{1}{50}< 2\)
\(\Rightarrow A< 2\)
Chúc bạn học tốt
ta có: \(\frac{1}{2^2}=\frac{1}{2.2}< \frac{1}{1.2};\frac{1}{3^2}=\frac{1}{3.3}< \frac{1}{2.3};\frac{1}{4^2}=\frac{1}{4.4}< \frac{1}{3.4};...;\frac{1}{100^2}=\frac{1}{100.100}< \frac{1}{99.100}\)
=>
285
= 28 . 28 . 28 . 28 . 28
= 784 . 784 . 28
= 614656 . 28
= 17210368
S=1/2.5+1/5.8+1/8.11+...+1/17.20
=1/3.(1/2-1/5/+1/5-1/8+1/8-1/11+...+1/17-1/20)
=1/3.(1/2-1/20)
=1/3.9/20
=3/20