M = 1/21 + 1/28+1/36+...+1/465
= 2/42+2/56+2/72+...+2/930
= 2.( 1/6.7 + 1/7.8 + 1/ 7.9 + ... + 1/30.31)
= 2.( 1/6-1/7+1/7-1/8+...+1/30-1/31)
= 2.(1/6 - 1/31) = 2.25/186 = 25/92
A=\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}\)
\(\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)
Tính Nhanh:
B=\(\dfrac{1}{2}\)+\(\dfrac{1}{4}\)+\(\dfrac{1}{8}\)+\(\dfrac{1}{16}\)+\(\dfrac{1}{32}\)+\(\dfrac{1}{64}\)
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tìm x thuộc N biết:
\(\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+....+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)
tính N =\(\dfrac{1}{2}\)+\(\dfrac{1}{2^2}\)+\(\dfrac{1}{2^3}\)+..... + \(\dfrac{1}{2^9}\)+\(\dfrac{1}{2^{10}}\)
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Chứng minh rằng :
1- \(\dfrac{1}{2^2}\) - \(\dfrac{1}{3^2}\) - … - \(\dfrac{1}{100^2}\) > \(\dfrac{1}{100}\)
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Bài 1.Tính
a)\(\dfrac{4}{28}\)+\(\dfrac{12}{36}\) b)\(\dfrac{-12}{18}\)+\(\dfrac{15}{-21}\) c)\(\dfrac{14}{28}\)-\(\dfrac{-16}{32}\)-\(\dfrac{17}{51}\)
Chứng minh A > B, biết:
A= \(\dfrac{2}{5.7}+\dfrac{5}{7.12}+\dfrac{7}{12.19}+\dfrac{9}{19.28}+\dfrac{11}{28.39}+\dfrac{1}{30.40}\)
B= \(\dfrac{1}{20}+\dfrac{1}{44}+\dfrac{1}{77}+\dfrac{1}{119}+\dfrac{1}{170}\)
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\(\dfrac{-28}{35}=\dfrac{16}{x}\)
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