Tìm x biết:
\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+...+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
cho
E = \(\frac{1}{1\cdot101}\) + \(\frac{1}{2\cdot102}\) + ...............+\(\frac{1}{10\cdot110}\)
F = \(\frac{1}{1\cdot11}\) + \(\frac{1}{2\cdot12}\) + ....................+\(\frac{1}{100\cdot110}\)
tính \(\frac{E}{F}\)
Tìm số nguyên x biết:
\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+...+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
a)A=\(\frac{1}{1\cdot3\cdot5}+\frac{1}{3\cdot5\cdot7}+\frac{1}{5\cdot7\cdot9}+...+\frac{1}{25\cdot27\cdot29}\)
b)\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+...+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1.11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
\(E=\frac{1}{1\times101}+\frac{1}{2\times102}+\frac{1}{3\times103}+.........+\frac{1}{10\times110}\) và \(F=\frac{1}{1\times11}+\frac{1}{2\times12}+\frac{1}{3\times13}+.......+\frac{1}{100\times110}\)
tìm tỉ số \(\frac{E}{F}\)
Tính A=\(\frac{\frac{1}{1\cdot300}+\frac{1}{2\cdot301}+\frac{1}{3\cdot302}+...+\frac{1}{101\cdot400}}{\frac{1}{1\cdot102}+\frac{1}{2\cdot103}+\frac{1}{3\cdot104}+...+\frac{1}{299\cdot400}}\)
bài 1 tính nhanh
a) A=\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{99\cdot101}\)
b) B=\(\frac{3}{1\cdot3}+\frac{3}{3\cdot5}+\frac{3}{57}+...+\frac{3}{49\cdot51}\)
c) C=\(\frac{5^2}{1\cdot6}+\frac{5^2}{6\cdot11}+\frac{5^2}{11\cdot16}+\frac{5^2}{16\cdot21}+\frac{5^2}{21\cdot26}+\frac{5^2}{26\cdot31}\)
d) D=\(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
e) E=\(\frac{3}{5\cdot11}+\frac{5}{11\cdot21}+\frac{7}{21\cdot35}+\frac{9}{35\cdot53}\)
f) F=\(\frac{2}{15}+\frac{2}{35}+\frac{2}{99}+\frac{4}{77}\)
giải chi tiết giúp mình nhé thank you very much
\(A=\frac{7}{10\cdot11}+\frac{7}{11\cdot12}+\frac{7}{12\cdot13}+...+\frac{7}{69\cdot70}\)
\(B=\frac{1}{25\cdot27}+\frac{1}{27\cdot29}+\frac{1}{29\cdot30}+...+\frac{1}{73\cdot75}\)
\(C=\frac{4}{2\cdot4}+\frac{4}{4\cdot6}+\frac{4}{6\cdot8}+...3+\frac{4}{2008\cdot2010}\)
a) Rút gọn:
\(\frac{\frac{1}{1\cdot300}+\frac{1}{2\cdot301}+\frac{1}{3\cdot302}+...+\frac{1}{101\cdot400}}{\frac{1}{1\cdot102}+\frac{1}{2\cdot103}+\frac{1}{3\cdot104}+...+\frac{1}{299\cdot400}}\)
b) CMR: \(1\cdot3\cdot5\cdot7\cdot9\cdot...\cdot197\cdot199\)= \(\frac{101}{2}\cdot\frac{102}{2}\cdot\frac{103}{2}\cdot...\cdot\frac{200}{2}\).
c) Cho: A=\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{199\cdot200}\).
B=\(\frac{1}{101\cdot200}+\frac{1}{102\cdot199}+...+\frac{1}{199\cdot102}+\frac{1}{200\cdot101}\).
d) Tìm số tự nhiên n lớn nhất có ba chữ số sao cho n chia 8 dư 7,chia 31 dư 28.
e) Tìm số nguyên tố \(\overline{ab}\) (a>0>b),sao cho \(\overline{ab}-\overline{ba}\)là số chính phương.