Tính A=13x15+15x17+17x19+...+99x101
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
=4x(\(\frac{1}{11x13}\)+\(\frac{1}{13x15}\)+.......+\(\frac{1}{99x101}\))
=4x(\(\frac{1}{11}\)-\(\frac{1}{13}\)+\(\frac{1}{13}\)-\(\frac{1}{15}\)+....+\(\frac{1}{99}\)-\(\frac{1}{101}\))
4x(\(\frac{1}{11}\)-\(\frac{1}{101}\))
=4x \(\frac{90}{1111}\)
=\(\frac{360}{1111}\)
\(\frac{4}{11\times13}+\frac{4}{13\times15}+\frac{4}{15\times17}+...+\frac{4}{99\times101}\)
\(=\frac{4}{11}-\frac{4}{13}+\frac{4}{13}-\frac{4}{15}+\frac{4}{15}-\frac{4}{17}+...+\frac{4}{99}-\frac{4}{101}\)
\(=\frac{4}{11}-\frac{4}{101}\)
\(=\frac{360}{1111}\)
A=\(\frac{4}{11}-\frac{4}{13}+\frac{4}{13}-\frac{4}{15}+...+\frac{4}{99}-\frac{4}{101}\)
\(A=4\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(A=4.\left(\frac{1}{11}-\frac{1}{101}\right)\)
A=4. 90/1111=360/1111
(1/11-1/13+1/13-1/15+.....+1/19-1/21)*462-y=19
(1/11-1/21)*462-y=19
10/231*462-y=19
20-y=19
y=1
\(\left(\frac{2}{11x13}+\frac{2}{13x15}+\frac{2}{15x17}+\frac{2}{17x19}+\frac{2}{19x21}\right)\)) x 462 - y = 19
\(=\left(\frac{13-11}{11x13}+\frac{15-13}{13x15}+\frac{17-15}{15x17}+\frac{19-17}{17x19}+\frac{21-19}{19x21}\right)\)x 462 - y = 19
\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\)) x 462 - y = 19
\(=\left(\frac{1}{11}-\frac{1}{21}\right)\)x 462 - y = 19
\(=\left(\frac{21}{231}-\frac{11}{231}\right)\)x 462 - y = 19
\(=\frac{10}{231}\)x 462 - y = 19
\(=20\)- y = 19
y = 20 - 19
y = 1
Tìm y biết \(\left(\frac{2}{11x13}+\frac{2}{13x15}+\frac{2}{15x17}+\frac{2}{17x19}\right)+462-y=19\)
ta lấy : (1/11-1/13+1/13-1/15+...+1/19)x462-y=19
(1/11-1/19)x462-y=19
32/209x462-y=19
70,73-y=19
y=70,73-19=51,73
đúng thì k cho mình nhé , ko đúng cũng ko sao ^^
\(A=13.15+15.17+17.19+...+99.101\)
\(\Rightarrow6A=13.15.6+15.17.6+17.19.6+...+99.101.6\)
\(\Rightarrow6A=13.15.\left(17-11\right)+15.17.\left(19-13\right)+17.19.\left(21-15\right)+...+99.101.\left(103-97\right)\)
\(\Rightarrow6A=\left(13.15.17-11.13.15\right)+\left(15.17.19-13.15.17\right)+\left(17.19.21-15.17.19\right)+...+\left(99.101.103-97.99.101\right)\)
\(\Rightarrow6A=99.101.103-11.13.15\)
\(\Rightarrow6A=1027752\)
\(\Rightarrow A=171292\)