Tính tổng
A=7+72 +73+...+7n-1+7n
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
14 tháng 1 2024
\(\dfrac{7}{8}+\dfrac{7}{120}+\dfrac{7}{360}+\dfrac{7}{\left(7n-6\right)\left(7n+1\right)}+\dfrac{1}{7n+1}\)
\(=\dfrac{7}{1\cdot8}+\dfrac{7}{8\cdot15}+\dfrac{7}{360}+\dfrac{1}{7n-6}-\dfrac{1}{7n+1}+\dfrac{1}{7n+1}\)
\(=1-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{15}+\dfrac{7}{360}+\dfrac{1}{7n-6}\)
\(=\dfrac{14}{15}+\dfrac{7}{360}+\dfrac{1}{7n-6}=\dfrac{343}{360}+\dfrac{1}{7n-6}\)
\(=\dfrac{343\left(7n-6\right)+360}{360\left(7n-6\right)}\)
\(=\dfrac{2401n-1698}{360\left(7n-6\right)}\)
H
14 tháng 1 2024
\(\dfrac{7}{8}+\dfrac{7}{120}+\dfrac{7}{360}+\dfrac{7}{\left(7n-6\right)\left(7n+1\right)}+\dfrac{1}{7n+1}\\ =\left(\dfrac{7}{8}+\dfrac{7}{120}+\dfrac{7}{360}\right)+\left(\dfrac{7}{\left(7n-6\right)\left(7n+1\right)}+\dfrac{1}{7n+1}\right)\\ =\left(\dfrac{315}{360}+\dfrac{21}{360}+\dfrac{7}{360}\right)+\left(\dfrac{7}{\left(7n-6\right)\left(7n+1\right)}+\dfrac{7n-6}{\left(7n+1\right)\left(7n-6\right)}\right)\)
\(=\dfrac{343}{360}+\dfrac{7n+1}{\left(7n-6\right)\left(7n+1\right)}\\ =\dfrac{343}{360}+\dfrac{1}{7n-6}\\ =\dfrac{343\left(7n-6\right)+360}{360\left(7n-6\right)}\\ =\dfrac{2401n-2058+360}{360\left(7n-6\right)}\\ =\dfrac{2401n-1698}{360\left(7n-6\right)}\)
NV
Nguyễn Việt Lâm
Giáo viên
14 tháng 1 2024
\(=\dfrac{7}{1.8}+\dfrac{7}{8.15}+\dfrac{7}{15.24}+...++\dfrac{7}{\left(7n-6\right)\left(7n+1\right)}+\dfrac{1}{7n+1}\)
\(=1-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{24}+...+\dfrac{1}{7n-6}-\dfrac{1}{7n+1}+\dfrac{1}{7n+1}\)
\(=1\)
NM
2
8 tháng 4 2018
Đặt \(A=\frac{4n+3}{7n+1}-\frac{3n-2}{7n+1}+\frac{2n-3}{7n+1}\) ta có :
\(A=\frac{4n+3-3n+2+2n-3}{7n+1}\)
\(A=\frac{3n+2}{7n+1}\)
Vậy \(A=\frac{3n+2}{7n+1}\)
Chúc bạn học tốt ~
VK
1
29 tháng 3 2017
\(\frac{19n+7}{7n+11}=2\)
\(\Rightarrow x=3\)
Còn cách giải thì k xong mình nói
\(\left(\frac{-.-}{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{_{ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}\right)\)
14 tháng 10 2023
Có: `343=7^3`.
`A=7^n(1+7+49)=3.19.343`
`<=> 7^n.3.19=3.19.7^3`.
`<=> n=3.`
Vậy `n=3`
KV
14 tháng 10 2023
7ⁿ + 7ⁿ⁺¹ + 7ⁿ⁺² = 3.19.343
7ⁿ.(1 + 7 + 7²) = 19551
7ⁿ.57 = 19551
7ⁿ = 19551 : 57
7ⁿ = 343
7ⁿ = 7³
n = 3
5 tháng 6 2022
a: \(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{\left(2n-1\right)\left(2n+1\right)}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2n-1}-\dfrac{1}{2n+1}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{2n+1-1}{2n+1}=\dfrac{1}{2}\cdot\dfrac{2n}{2n+1}=\dfrac{n}{2n+1}\)
b: \(=\dfrac{1}{4}\left(\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+...+\dfrac{4}{\left(4n-3\right)\left(4n+1\right)}\right)\)
\(=\dfrac{1}{4}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{4n-3}-\dfrac{1}{4n+1}\right)\)
\(=\dfrac{1}{4}\cdot\dfrac{4n}{4n+1}=\dfrac{n}{4n+1}\)
7 tháng 6 2022
a: \(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{\left(2n-1\right)\left(2n+1\right)}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2n-1}-\dfrac{1}{2n+1}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{2n+1-1}{2n+1}\)
\(=\dfrac{n}{2n+1}\)
b: \(=\dfrac{1}{4}\left(\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+...+\dfrac{4}{\left(4n-3\right)\left(4n+1\right)}\right)\)
\(=\dfrac{1}{4}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{4n-3}-\dfrac{1}{4n+1}\right)\)
\(=\dfrac{1}{4}\cdot\dfrac{4n}{4n+1}=\dfrac{n}{4n+1}\)
A=7+72 +73+...+7n-1+7n
7A = 72 + 73 + 74 + ... + 7n + 7n+1
7A - A = ( 72 + 73 + 74 + ... + 7n + 7n+1 ) - ( 7+72 +73+...+7n-1+7n )
6A = 7n+1 - 7
A = \(\frac{7^{n+1}-7}{6}\)