Các câu hỏi tương tự
Tìm x biết:
\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+...+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
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=\(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+\frac{1}{3\cdot103}+...+\frac{1}{10\cdot110}\)và F=\(\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+\frac{1}{3\cdot13}+...+\frac{1}{100\cdot110}\)
tính tỉ số\(\frac{E}{F}\)
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 x biết:
a) \(\frac{1}{5\cdot8}\) + \(\frac{1}{8\cdot11}\) + \(\frac{1}{11\cdot14}\) + .....+ \(\frac{1}{x\cdot\left(x+3\right)}\) = \(\frac{101}{1540}\)
b) \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\cdot\left(x+1\right):2}=1\frac{1991}{1993}\)
Tính
A=\(\left(1-\frac{1}{21}\right)\cdot\left(1-\frac{1}{28}\right)\cdot\left(1-\frac{1}{36}\right)\cdot....\cdot\left(1-\frac{1}{1326}\right)\)
B=\(\left(1+\frac{1}{1\cdot3}\right)\cdot\left(1+\frac{1}{2\cdot4}\right)\cdot\left(1+\frac{1}{3\cdot5}\right)\cdot....\cdot\left(1+\frac{1}{99\cdot101}\right)\)
Tính nhanh :
\(A=\left(1-\frac{2}{6\cdot7}\right)\left(1-\frac{2}{7\cdot8}\right)\left(1-\frac{2}{8\cdot9}\right)\cdot\cdot\cdot\left(1-\frac{2}{51\cdot52}\right)\)
\(B=\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\left(1+\frac{1}{3\cdot5}\right)\cdot\cdot\cdot\left(1+\frac{1}{99\cdot101}\right)\)
a) Rút gọn:frac{frac{1}{1cdot300}+frac{1}{2cdot301}+frac{1}{3cdot302}+...+frac{1}{101cdot400}}{frac{1}{1cdot102}+frac{1}{2cdot103}+frac{1}{3cdot104}+...+frac{1}{299cdot400}}b) CMR: 1cdot3cdot5cdot7cdot9cdot...cdot197cdot199 frac{101}{2}cdotfrac{102}{2}cdotfrac{103}{2}cdot...cdotfrac{200}{2}.c) Cho: Afrac{1}{1cdot2}+frac{1}{2cdot3}+frac{1}{3cdot4}+...+frac{1}{199cdot200}. Bfrac{1}{101cdot200}+frac{1}{102cdot199}+...+frac{1}{199cdot102}+frac{1}{200cdot101}.d) Tìm số tự nhiên n lớn nhất có ba ch...
Đọc tiếp
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.
a) Tính
\(A=\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot\cdot\cdot\left(1-\frac{1}{2014}\right)\cdot\left(1-\frac{1}{2015}\right)\cdot\left(1-\frac{1}{2016}\right)\)
b) Tìm x:
\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x-2}{42}+\frac{x-2}{56}+\frac{x-2}{72}=\frac{16}{9}\)