Đặt A = 1/1.3 + 1/3.5 + 1/5.7 +........+ 1/(2n - 1)(2n + 1)
2.A = 2/1.3 + 2/3.5 + 2/5.7 +........+ 2/(2n - 1)(2n + 1)
2.A = 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ..... + 1/(2n - 1) - 1/(2n + 1)
2.A = 1 - 1/(2n + 1) = 2n/(2n + 1)
Vậy A = n/(2n + 1)
hình như sai!!
Chứng minh rằng
\(\frac{1\cdot3\cdot5\cdot\cdot\cdot\left(2n-1\right)}{\left(n+1\right)\cdot\left(n+2\right)\cdot\left(n+3\right)\cdot...\cdot2n}=\frac{1}{2^n}\)
Chứng minh rằng:
a)\(\frac{1\cdot3\cdot5\cdot\cdot\cdot39}{21\cdot22\cdot23\cdot\cdot\cdot40}=\frac{1}{2^{20}}\)
b)\(\frac{1\cdot3\cdot5\cdot\cdot\cdot\left(2n-1\right)}{\left(n+1\right)\left(n+2\right)\left(n+3\right)\cdot\cdot\cdot2n}=\frac{1}{2^n}\)Với \(n\inℕ^∗\)
Chứng minh rằng :
\(\frac{1\cdot3\cdot5\cdot...\cdot\left(2n-1\right)}{\left(n+1\right)\cdot\left(n+2\right)\cdot\left(n+3\right)\cdot...\cdot2n}=\frac{1}{2^n}\)
\(\frac{1\cdot3\cdot5\cdot.....\left(2n-1\right)}{\left(n+1\right)\left(n+2\right)\left(n+3\right)....2n}\)=\(\frac{1}{2^n}\)với n \(\varepsilon\)N*
Tính nhanh :
\(A=\left(1-\frac{2}{6\cdot7}\right)\left(1-\frac{2}{7\cdot8}\right)\left(1-\frac{2}{8\cdot9}\right)\cdot\cdot\cdot\left(1-\frac{2}{51\cdot52}\right)\)
\(B=\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\left(1+\frac{1}{3\cdot5}\right)\cdot\cdot\cdot\left(1+\frac{1}{99\cdot101}\right)\)
bài 1 tính tổng
a) \(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{99\cdot101}\)
b) \(\frac{5}{1\cdot3}+\frac{5}{3\cdot5}+\frac{5}{5\cdot7}+...+\frac{5}{99\cdot101}\)
bài 2 chứng tỏ rằng phân số \(\frac{2n+1}{3n+2}\)là phân số tối giản.
bài 3 cho A=\(\frac{n+2}{n-5}\)(n thuộc z;n khác 5) tìm x để A thuộc z
bài 4 tính giá trị biểu thức
A=\(10101\cdot\left(\frac{5}{111111}+\frac{5}{222222}-\frac{4}{3\cdot7\cdot11\cdot13\cdot37}\right)\)
a)A=\(\frac{1}{1\cdot3\cdot5}+\frac{1}{3\cdot5\cdot7}+\frac{1}{5\cdot7\cdot9}+...+\frac{1}{25\cdot27\cdot29}\)
b)\(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+...+\frac{1}{10\cdot110}\right)\cdot x=\frac{1}{1.11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)
Tính tổng :
a) \(\frac{1}{3\cdot5\cdot7}+\frac{1}{5\cdot7\cdot9}+\frac{1}{7\cdot9\cdot11}+...+\frac{1}{2013\cdot2015\cdot2017}\)
b) \(\left(1-\frac{1}{2^2}\right)\cdot\left(1-\frac{1}{3^2}\right)\cdot\left(1-\frac{1}{4^2}\right)\cdot...\cdot\left(1-\frac{1}{2017^2}\right)\)
c) \(\left(1-\frac{1}{1+2}\right)\cdot\left(1-\frac{1}{1+2+3}\right)\cdot...\cdot\left(1-\frac{1}{1+2+3+...+2017}\right)\)
\(D=\left(1+\frac{1}{1\cdot3}\right)\cdot\left(1+\frac{1}{2\cdot4}\right)\cdot\left(1+\frac{1}{3\cdot5}\right)...\left(1+\frac{1}{99.100}\right)\)
