41+30+38+55=
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34 < 38 55 < 57 90 = 90
36 > 30 55 = 55 97 > 92
37 = 37 55 > 51 92 < 97
25 < 30 85 < 95 48 > 42
a,số các số hạng là
41-5 :3 + 1 = 13
tổng là
(5 + 41 )x 13 : 2 = 299
b, tổng = -106
a) \(\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}\)
\(=1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+1-\frac{1}{30}+1-\frac{1}{42}+1-\frac{1}{56}+1-\frac{1}{72}+1-\frac{1}{90}\)
\(=8-\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)
\(=8-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(=8-\left(\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+\frac{6-5}{5.6}+\frac{7-6}{6.7}+\frac{8-7}{7.8}+\frac{9-8}{8.9}+\frac{10-9}{9.10}\right)\)
\(=8-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(=8-\left(\frac{1}{2}-\frac{1}{10}\right)=7,6\)
b) Bạn làm tương tự.
\(\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)
\(=1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)
\(=8-\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)
\(=8-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)
\(=8-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)\)
\(=8-\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=\frac{38}{5}\)
A = \(\dfrac{1}{2}\) + \(\dfrac{5}{6}\) + \(\dfrac{11}{12}\) + \(\dfrac{19}{20}\) + \(\dfrac{29}{30}\) + \(\dfrac{41}{42}\) + \(\dfrac{55}{56}\)
A = (1 - \(\dfrac{1}{2}\)) + ( 1 - \(\dfrac{1}{6}\)) + (1 - \(\dfrac{1}{12}\)) + (1 - \(\dfrac{1}{20}\)) +(1-\(\dfrac{1}{30}\))+(1-\(\dfrac{1}{42}\))+(1-\(\dfrac{1}{56}\))
A = (1 + 1+1 + 1 + 1+1+1)- (\(\dfrac{1}{2}\)+\(\dfrac{1}{6}\)+\(\dfrac{1}{12}\)+\(\dfrac{1}{20}\)+\(\dfrac{1}{30}\)+\(\dfrac{1}{42}\)+\(\dfrac{1}{56}\))
A = 7 - (\(\dfrac{1}{1\times2}\)+\(\dfrac{1}{2\times3}\)+\(\dfrac{1}{3\times4}\)+\(\dfrac{1}{4\times5}\)+\(\dfrac{1}{5\times6}\)+\(\dfrac{1}{6\times7}\)+\(\dfrac{1}{7\times8}\))
A = 7 - (\(\dfrac{1}{1}\) - \(\dfrac{1}{2}\)+ \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\)+\(\dfrac{1}{6}\)-\(\dfrac{1}{7}\)+\(\dfrac{1}{7}\)-\(\dfrac{1}{8}\))
A = 7 - (\(\dfrac{1}{1}\) - \(\dfrac{1}{8}\))
A = 7 - \(\dfrac{7}{8}\)
A = \(\dfrac{49}{8}\)
1/2+...................+71/72
=(1-1/2)+......................+(1-1/72)
=1+1+.....+1-1/2-...................-1/72
=8-(1/2+...................+1/72)
=8-(2-1/1*2+3-2/2*3+.............+9-8/8*9)
=8-(1-1/2+1/2-1/3+1/3-..............+1/8-1/9)
=8-(1-1/9)
=8-8/9
=64/9
\(=1-\dfrac{1}{2}+1-\dfrac{1}{6}+1-\dfrac{1}{12}+1-\dfrac{1}{20}+1-\dfrac{1}{30}+1-\dfrac{1}{42}+1-\dfrac{1}{56}\)
\(=7-\left(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{56}\right)\)
\(=7-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{7}-\dfrac{1}{8}\right)\)
\(=7-\dfrac{7}{8}=\dfrac{49}{8}\)
=164 nha
Đáp án:
=164
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