Tính \(2.5+1.4-1\dfrac{3}{7}\)
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
NV
Nguyễn Việt Lâm
Giáo viên
1 tháng 12 2018
\(A=\left(\dfrac{6}{1.4}\right)\left(\dfrac{12}{2.5}\right)\left(\dfrac{20}{3.6}\right)\left(\dfrac{x^2+3x+2}{x\left(x+3\right)}\right)\)
\(A=\dfrac{2.3}{1.4}.\dfrac{3.4}{2.5}.\dfrac{4.5}{3.6}...\dfrac{\left(x+1\right)\left(x+2\right)}{x\left(x+3\right)}\)
\(A=\dfrac{2.3.4...\left(x+1\right)}{1.2.3...x}.\dfrac{3.4.5...\left(x+2\right)}{4.5.6...\left(x+3\right)}=\left(x+1\right)\dfrac{3}{x+3}=\dfrac{3\left(x+1\right)}{x+3}\)
M
29 tháng 10 2017
Đặt 1.4+2.5+.....+n.(n+3)=C
Hướng dẫn: 3C = 3.[1.2 +2.3 +3.4 + ... + n(n + 1)] + 3.(2 + 4 + 6 + ... + 2n)
= 1.2.3 + 2.3.3 + 3.4.3 + ... + n(n + 1).3 + 3.(2 + 4 + 6 + ... + 2n)
Nên C = n(n+1)(n+5):3
29 tháng 10 2017
\(\frac{1.5.6+2.10.12+4.20.24+9.45.54}{1.3.5+2.6+4.12.20+9.27.45}\)
MH
6 tháng 2 2022
\(\dfrac{6}{11}.\dfrac{3}{7}+\dfrac{3}{7}.\dfrac{5}{11}\)
\(=\dfrac{3}{7}.\left(\dfrac{6}{11}+\dfrac{5}{11}\right)\)
\(=\dfrac{3}{7}.1=\dfrac{3}{7}\)
13 tháng 11 2023
\(B=1\cdot2\cdot3+2\cdot3\cdot4+...+\left(n-1\right)\cdot n\cdot\left(n+1\right)\)
=>\(4B=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot4+...+\left(n-1\right)\cdot n\left(n+1\right)\cdot4\)
=>\(4B=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\left(5-1\right)+...+\left(n-1\right)\cdot n\left(n+1\right)\left[\left(n+2\right)-\left(n-2\right)\right]\)
=>\(4B=1\cdot2\cdot3\cdot4-1\cdot2\cdot3\cdot4+...+\left(n-2\right)\left(n-1\right)\cdot n\cdot\left(n+1\right)-\left(n-2\right)\cdot\left(n-1\right)\cdot n\cdot\left(n+1\right)+\left(n-1\right)\cdot n\left(n+1\right)\left(n+2\right)\)
=>\(4B=\left(n-1\right)\cdot n\cdot\left(n+1\right)\left(n+2\right)\)
=>\(B=\dfrac{\left(n-1\right)\cdot n\left(n+1\right)\left(n+2\right)}{4}\)
\(C=1\cdot4+2\cdot5+3\cdot6+...+n\left(n+3\right)\)
\(=1\cdot\left(1+3\right)+2\left(2+3\right)+...+n\left(n+3\right)\)
\(=\left(1^2+2^2+...+n^2\right)+3\left(1+2+...+n\right)\)
\(=\dfrac{n\left(n+1\right)\left(2n+1\right)}{6}+3\cdot\dfrac{n\left(n+1\right)}{2}\)
\(=\dfrac{n\left(n+1\right)\left(2n+1\right)}{6}+\dfrac{3n\left(n+1\right)}{2}\)
\(=\dfrac{n\left(n+1\right)}{2}\cdot\left(\dfrac{2n+1}{3}+3\right)\)
\(=\dfrac{n\left(n+1\right)}{2}\cdot\dfrac{2n+1+9}{3}\)
\(=\dfrac{n\left(n+1\right)\left(n+5\right)}{3}\)
\(D=1^2+2^2+...+n^2\)
\(=1+\left(1+1\right)\cdot2+\left(1+2\right)\cdot3+...+\left(1+n-1\right)\cdot n\)
\(=1+2+3+...+n+\left(1\cdot2+2\cdot3+...+\left(n-1\right)\cdot n\right)\)
Đặt \(A=1+2+3+...+n;E=1\cdot2+2\cdot3+...+\left(n-1\right)\cdot n\)
\(E=1\cdot2+2\cdot3+...+\left(n-1\right)\cdot n\)
=>\(3E=1\cdot2\cdot3+2\cdot3\cdot3+...+\left(n-1\right)\cdot n\cdot3\)
=>\(3E=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+\left(n-1\right)\cdot n\left[\left(n+1\right)-\left(n-2\right)\right]\)
=>\(3E=1\cdot2\cdot3-1\cdot2\cdot3+2\cdot3\cdot4+...+\left(n-1\right)\cdot n\left(n-2\right)-\left(n-1\right)\cdot n\left(n-2\right)+\left(n-1\right)\cdot n\cdot\left(n+1\right)\)
=>\(3E=\left(n-1\right)\cdot n\left(n+1\right)=n^3-n\)
=>\(E=\dfrac{n^3-n}{3}\)
\(A=1+2+3+...+n\)
Số số hạng là n-1+1=n(số)
Tổng của dãy số là: \(A=\dfrac{n\left(n+1\right)}{2}\)
=>\(D=\dfrac{n^3-n}{3}+\dfrac{n\left(n+1\right)}{2}\)
\(=\dfrac{2n^3-2n+3n^2+3n}{6}\)
=>\(D=\dfrac{2n^3+3n^2+n}{6}\)
1 tháng 1 2024
\(A=1\cdot4+2\cdot5+3\cdot6+...+n\left(n+3\right)\)
\(=1\left(1+3\right)+2\left(2+3\right)+3\left(3+3\right)+...+n\left(n+3\right)\)
\(=\left(1^2+2^2+...+n^2\right)+3\left(1+2+3+...+n\right)\)
\(=\dfrac{n\left(n+1\right)\left(2n+1\right)}{6}+3\cdot\dfrac{n\left(n+1\right)}{2}\)
\(=\dfrac{n\left(n+1\right)\left(2n+1\right)+9n\left(n+1\right)}{6}\)
\(=\dfrac{n\left(n+1\right)\left(2n+1+9\right)}{6}\)
\(=\dfrac{n\left(n+1\right)\left(2n+10\right)}{6}=\dfrac{n\left(n+1\right)\left(n+5\right)}{3}\)
2
22 tháng 5 2021
Ta thấy: 1.4 = 1.(1 + 3)
2.5 = 2.(2 + 3)
3.6 = 3.(3 + 3)
4.7 = 4.(4 + 3)
…….
n(n + 3) = n(n + 1) + 2n
Vậy C = 1.2 + 2.1 + 2.3 + 2.2 + 3.4 + 2.3 + … + n(n + 1) +2n
C = 1.2 + 2 +2.3 + 4 + 3.4 + 6 + … + n(n + 1) + 2n
C = [1.2 +2.3 +3.4 + … + n(n + 1)] + (2 + 4 + 6 + … + 2n)
⇒ 3C = 3.[1.2 +2.3 +3.4 + … + n(n + 1)] + 3.(2 + 4 + 6 + … + 2n)
3C = 1.2.3 + 2.3.3 + 3.4.3 + … + n(n + 1).3 + 3.(2 + 4 + 6 + … + 2n)
3C = n(n + 1)(n + 2) +
⇒ C = +
=
\(2.5+1.4-1\dfrac{3}{7}=\dfrac{5}{2}+\dfrac{7}{5}-\dfrac{10}{7}=\dfrac{5\cdot35}{2\cdot35}+\dfrac{7\cdot14}{5\cdot14}-\dfrac{10\cdot10}{7\cdot10}=\dfrac{175}{70}+\dfrac{98}{70}-\dfrac{100}{70}=\dfrac{173}{70}\)
2,5 + 1,4 - \(1\dfrac{3}{7}\)
=3,9 + \(\dfrac{10}{7}\)
=\(\dfrac{373}{70}\)