Violympic toán 6
Các câu hỏi tương tự
Bài 1:So sánh Avà B biết rằng:
Afrac{10^{15}+1}{10^{16}+1}; Bfrac{10^{16}+1}{10^{17}+1}
Afrac{3}{8^3}+frac{7}{8^4}; Bfrac{7}{8^3}+frac{3}{8^4}
Afrac{1}{11}+frac{1}{12}+frac{1}{13}+.......+frac{1}{19}+frac{1}{20}; Bfrac{1}{2}
Bài 2:Dạng tính tổng đặc biệt:
Afrac{1}{1cdot2}+frac{1}{2cdot3}+frac{1}{3cdot4}+.....+frac{1}{99cdot100}
Bfrac{2}{1cdot3}+frac{2}{3cdot5}+frac{2}{5cdot7}+.....+frac{2}{99cdot101}
Cfrac{3^2}{10}+frac{3^2}{40}+frac{3^2}{88}+......+frac{3^2}{340}
Dfrac{1}{...
Đọc tiếp
Bài 1:So sánh Avà B biết rằng:
A=\(\frac{10^{15}+1}{10^{16}+1};\) B=\(\frac{10^{16}+1}{10^{17}+1}\)
A=\(\frac{3}{8^3}+\frac{7}{8^4}\); B=\(\frac{7}{8^3}+\frac{3}{8^4}\)
A=\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+.......+\frac{1}{19}+\frac{1}{20};\) B=\(\frac{1}{2}\)
Bài 2:Dạng tính tổng đặc biệt:
\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+.....+\frac{1}{99\cdot100}\)
\(B=\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+.....+\frac{2}{99\cdot101}\)
\(C=\frac{3^2}{10}+\frac{3^2}{40}+\frac{3^2}{88}+......+\frac{3^2}{340}\)
\(D=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+......+\frac{1}{3^8}\)
\(E=\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{99}\right)\)
Bài 3:Dạng chứng minh:
\(A=1+\frac{1}{2}+\frac{1}{3}+......+\frac{1}{99}.\)Chứng minh rằng A chia hết cho 100
A=\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{70}\).Chứng minh rằng A>\(\frac{4}{3}\)
Cho A=\(\frac{1}{3^2}+\frac{1}{5^5}+\frac{1}{7^2}+...+\frac{1}{2019^2}\)
Chứng minh A<\(\frac{1}{2}\)
21 tháng 4 2019 lúc 21:03
a) Chứng minh: \(\frac{11}{15}< \frac{1}{21}+\frac{1}{22}+\frac{1}{23}+...+\frac{1}{60}< \frac{3}{2}\)
b) Chứng minh: \(3< 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}< 6\)
1.chứng minh rằng Afrac{1}{16} biết Afrac{1}{5^2}+frac{2}{5^3}+frac{3}{5^4}+.....+frac{99}{5^{100}}
2.tính (M-N)^3 biết:
M1-frac{1}{2}+frac{1}{3}-frac{1}{4}+.....+frac{1}{2017}-frac{1}{2018}+frac{1}{2019}
Nfrac{1}{1010}+frac{1}{1011}+.....+frac{1}{2019}
Đọc tiếp
1.chứng minh rằng A<\(\frac{1}{16}\) biết A=\(\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+.....+\frac{99}{5^{100}}\)
2.tính (M-N)\(^3\) biết:
M=1-\(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{2017}-\frac{1}{2018}+\frac{1}{2019}\)
N=\(\frac{1}{1010}+\frac{1}{1011}+.....+\frac{1}{2019}\)
1.tính các biểu thức sau bằng một cách hợp lí
a.frac{108}{119}.frac{107}{211}+frac{108}{119}.frac{104}{211}
b.frac{15}{19}.frac{27}{33}+frac{15}{19}.frac{19}{33}-frac{15}{19}.frac{13}{33}
c.frac{-4}{5}.frac{13}{10}+frac{-4}{5}.frac{7}{10}-frac{-4}{5}
d.frac{frac{-2}{7}-frac{-2}{15}+frac{-2}{39}}{frac{5}{7}-frac{5}{15}+frac{5}{39}}
e.frac{3}{5}.frac{15}{7}-frac{15}{7}.frac{8}{5}
f.frac{2}{3}+frac{1}{3}.left(frac{-4}{9}+frac{5}{6}right):frac{7}{12}
h.frac{frac{3}{5}+frac{3}{7}-frac{3}{11}}{...
Đọc tiếp
1.tính các biểu thức sau bằng một cách hợp lí
a.\(\frac{108}{119}.\frac{107}{211}+\frac{108}{119}.\frac{104}{211}\)
b.\(\frac{15}{19}.\frac{27}{33}+\frac{15}{19}.\frac{19}{33}-\frac{15}{19}.\frac{13}{33}\)
c.\(\frac{-4}{5}.\frac{13}{10}+\frac{-4}{5}.\frac{7}{10}-\frac{-4}{5}\)
d.\(\frac{\frac{-2}{7}-\frac{-2}{15}+\frac{-2}{39}}{\frac{5}{7}-\frac{5}{15}+\frac{5}{39}}\)
e.\(\frac{3}{5}.\frac{15}{7}-\frac{15}{7}.\frac{8}{5}\)
f.\(\frac{2}{3}+\frac{1}{3}.\left(\frac{-4}{9}+\frac{5}{6}\right):\frac{7}{12}\)
h.\(\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{11}}\)
g.\(\frac{3}{-4}+\frac{2}{7}+\frac{-1}{4}+\frac{5}{7}+\frac{21}{22}.\frac{66}{7}\)
k.\(\frac{27.18+27.103-120.27}{15.33+33.12}\)
l.\(\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{4}{11}}\)
thực hiện các phép tính sau:
A =\(\frac{5.2^{30}.3^{18}-4.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)
B = 1 - 3 + 5 - 7 + 9 - 11 + ..... + 2017 - 2019
C =\(\left(\frac{151515}{606060}+\frac{151515}{121212}+\frac{151515}{202020}+\frac{151515}{303030}+\frac{151515}{424242}\right).\frac{28}{15}\)
Cho M =\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}\) .Hãy chứng minh M<\(\frac{3}{16}\)
Câu 2 Chứng minh rằng :
\(\frac{1}{7^2}-\frac{1}{7^4}+...+\frac{1}{7^{98}}-\frac{1}{7^{100}}< \frac{1}{50}\)
Tính nhanh
\(\frac{\frac{2}{5}+\frac{2}{7}+\frac{2}{9}+\frac{2}{11}+\frac{2}{13}}{\frac{3}{5}+\frac{3}{7}+\frac{3}{9}+\frac{3}{11}+\frac{3}{13}}+\frac{15151515}{45454545}\)
a,1frac{13}{15}.0,75-left(frac{8}{15}+0,25right).frac{24}{47}
b,5:left(4frac{3}{4}-1frac{25}{28}right)-1frac{3}{8}:left(frac{3}{8}+frac{9}{20}right)
c,6frac{5}{12}:2frac{3}{4}+11frac{1}{4}.left(frac{1}{3}-frac{1}{5}right)
d,left(frac{3}{5}+0,415-frac{3}{200}right).2frac{2}{3}.0,25
e,left(frac{3}{8}+frac{-3}{4}+frac{7}{12}right):frac{5}{6}+frac{1}{2}
g,1frac{13}{15}.0,75-left(frac{11}{20}+25%right);frac{7}{3}
Đọc tiếp
\(a,1\frac{13}{15}.0,75-\left(\frac{8}{15}+0,25\right).\frac{24}{47}\)
\(b,5:\left(4\frac{3}{4}-1\frac{25}{28}\right)-1\frac{3}{8}:\left(\frac{3}{8}+\frac{9}{20}\right)\)
\(c,6\frac{5}{12}:2\frac{3}{4}+11\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{5}\right)\)
\(d,\left(\frac{3}{5}+0,415-\frac{3}{200}\right).2\frac{2}{3}.0,25\)
\(e,\left(\frac{3}{8}+\frac{-3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
\(g,1\frac{13}{15}.0,75-\left(\frac{11}{20}+25\%\right);\frac{7}{3}\)