Giúp với ạ
2/1x3 + 2/3x5 + 2/5x7 +...+2/15x17 + 2/17x19
1/1x3+1/3x5+1/5x7+...+1/17x19 giúp mình nha
`1/[1xx3]+1/[3xx5]+1/[5xx7]+...+1/[17xx19]`
`=1/2xx(2/[1xx3]+2/[3xx5]+....+2/[17xx19])`
`=1/2xx(1-1/3+1/3-1/5+....+1/17-1/19)`
`=1/2xx(1-1/19)`
`=1/2xx18/19`
`=9/19`
Tính nhanh :\(\dfrac{2}{1X3}\) + \(\dfrac{2}{3X5}\) + \(\dfrac{2}{5X7}\) + ........ +\(\dfrac{2}{13X15}\) + \(\dfrac{2}{15X17}\) =
GHI RÕ CÁCH GIẢI RA HỘ MÌNH NHA
CẢM ƠN NHIỀU~~~~~~~
\(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+...+\dfrac{2}{13\times15}+\dfrac{2}{15\times17}\)
\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{13}-\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{17}\)
\(=1-\dfrac{1}{17}\)
\(=\dfrac{16}{17}\)
\(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{15\cdot17}\)
\(=2-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{15}-\dfrac{1}{17}\)
\(=2-\dfrac{1}{17}\)
\(=\dfrac{33}{17}\)
Tính nhanh:
a. 1/42 + 1/30 + 1/20 + 1/12 + 1/6 + 1/2
b. 2/1x3 + 2/3x5 + 2/5x7 +...+ 2/13x15 +2/15x17
giup minh 4/1x3+4/3x5+4/5x7+4/7x9+....+4/17x19+4/19x21
Ta có;\(\frac{4}{1\times3}+\frac{4}{3\times5}+\frac{4}{5\times7}+....+\frac{4}{19\times21}\)
\(=2\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+....+\frac{2}{19\times21}\right)\)
\(=2\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(=2\times\left(1-\frac{1}{21}\right)=2\times\frac{20}{21}=\frac{40}{21}\)
4/1 x 3 + 4/ 3 x 5 + 4/ 5 x 7 + ....+ 4/ 17 x 19 + 4/ 19 x 21
= 2 x ( 2/ 1 x 3 + 2/ 3 x 5 + 2/ 5 x 7 + ...+ 2/ 17 x 19 + 2/ 19 x 21 )
= 2 x ( 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ...+ 1/17 - 1/19 + 1/19 - 1/21 )
= 2 x ( 1 - 1/21 )
= 2 x 20/21
= 40/21
Chúc bạn học giỏi !!!
Đặt \(K=\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+\frac{4}{7.9}+...+\frac{4}{17.19}+\frac{4}{19.21}\)
\(\Leftrightarrow K=\left(\frac{4}{1}-\frac{4}{3}\right)+\left(\frac{4}{3}-\frac{4}{5}\right)+\left(\frac{4}{5}-\frac{4}{7}\right)+\left(\frac{4}{7}-\frac{4}{9}\right)+...+\left(\frac{4}{19}-\frac{4}{21}\right)\)
\(\Leftrightarrow K=\frac{4}{1}-\frac{4}{3}+\frac{4}{3}-\frac{4}{5}+\frac{4}{5}-\frac{4}{7}+\frac{4}{7}-\frac{4}{9}+...+\frac{4}{19}-\frac{4}{21}\)
\(\Leftrightarrow K=\frac{4}{1}-\frac{4}{21}=\frac{84}{21}-\frac{4}{21}=\frac{80}{21}\)
2/3x5+2/5x7+...+2/17x19
\(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{17.19}\)
= \(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{17}-\frac{1}{19}\)
= \(\frac{1}{3}-\frac{1}{19}\)
= \(\frac{16}{57}\)
\(\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{17.19}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.....+\frac{1}{17}-\frac{1}{19}\)
\(=\frac{1}{3}-\frac{1}{19}\)
\(=\frac{19}{57}-\frac{3}{57}\)
\(=\frac{16}{57}\)
vậy ......
chúc bạn học tốt!
\(\dfrac{2}{1x3}\)+\(\dfrac{3}{3x5}\)+\(\dfrac{2}{5x7}\)+....+\(\dfrac{2}{99x101}\)
giúp mình với ạ
`2/(1xx3)+2/(3xx5)+2/(5xx7)+...+2/(99xx101)` đề phải ntn chứ mà nhỉ
`=1/1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101`
`=1/1-1/101`
`=101/101-1/101`
`=100/101`
(Sửa phần 3 / 3 x 5 = 2 / 3 x 5)
\(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+...+\dfrac{2}{99\times101}\)
Ta có: \(=2\times\left(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+...+\dfrac{1}{99\times101}\right)\)
\(=2\times\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)
\(=2\times\left(1-\dfrac{1}{101}\right)\)
\(=2\times\dfrac{100}{101}\)
\(=\dfrac{200}{101}\)
Sửa bài ( dòng 3 đến hết bài )
... = \(2\times\dfrac{1}{2}\times\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)
\(=1-\dfrac{1}{101}\)
\(=\dfrac{100}{101}\)
a, 2/1x3 + 2/3x5 + 2/5x7 + 2/7x9 +...+ 9/913 x 215
b,1/1x3 + 1/3x5 + 1/5x7 + 1/7x9 + 1/213 x 215
[ Giúp mik với mấy bạn ơi ai nhanh mình sẽ tick nha TvT ]
( Toán tính nhanh nha )
sửa đề câu a và câu b nhá , mik nghĩ đề như này :
\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{213\cdot215}\)
\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{213}-\frac{1}{215}\)
= \(\frac{1}{1}-\frac{1}{215}\)
\(=\frac{214}{215}\)
b, đặt \(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{213\cdot215}\)
\(A\cdot2=\frac{2}{1\cdot3}+\frac{2}{3.5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{213\cdot215}\)
\(A\cdot2=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{213}-\frac{1}{215}\)
\(A\cdot2=\frac{1}{1}-\frac{1}{215}\)
\(A\cdot2=\frac{214}{215}\)
\(A=\frac{214}{215}:2\)
\(A=\frac{107}{215}\)
@ミ★Ŧɦươйǥ★彡 cảm ơn bạn nhiều
trả lời hiền thương đề bài của bạn ấy là đúm gòi nha
\(\dfrac{2}{1x3}+\dfrac{2}{3x5}+\dfrac{2}{5x7}+\dfrac{2}{7x9}+\dfrac{2}{9x11}\)
giúp mik với ạk
\(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+\dfrac{2}{9\times11}\)
\(=2\times\left(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}+\dfrac{1}{9\times11}\right)\)
\(=2\times\dfrac{1}{2}\times\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\right)\)
\(=1-\dfrac{1}{11}\)
\(=\dfrac{11}{11}-\dfrac{1}{11}\)
\(=\dfrac{10}{11}\)
\(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+\dfrac{2}{9\times11}\\ =1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\\ =1-\dfrac{1}{11}\\ =\dfrac{10}{11}\)
\(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{9\cdot11}\)
\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{2}{11}\)
\(=1-\dfrac{2}{11}\)
\(=\dfrac{9}{11}\)
Tìm x biết:
(1/3x5+1/5x7+ 1/7x9+ 1/9x11+1/11x13+1/13x15+ 1/15x17+ 1/17x19+1/19x21)xX=9/7
Làm giúp mk nha, cảm ơn các bạn chi cần ghi đáp số thôi nhé
Nhưng bn ơiX là x^2 hay tách biệt nếu tách biệt thì là 9/49 còn nếu là x^2 thì là 3/7 nhé
\(=\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)xX=\frac{9}{7} \)\(=\left(\frac{1}{3}-\frac{1}{21}\right)xX=\frac{9}{7}\)\(=\frac{2}{7}xX=\frac{9}{7}\)
\(X=\frac{9}{7}:\frac{2}{7}\)
\(X=\frac{9}{2}\)