What is the largest interger less than or equal to the expression\(\frac{1}{\frac{1}{1985}+\frac{1}{1986}+\frac{1}{1987}+...+\frac{1}{2015}}\)?
Hãy tìm A biết A là số lớn nhất với điều kiện sau:
A\(\le\)B
B=\(\frac{1}{\frac{1}{1985}+\frac{1}{1986}+\frac{1}{1987}+...+\frac{1}{2015}}\)
\(\frac{x-1986-1987}{1985}+\frac{x-1985-1987}{1986}+\frac{x-1985-1986}{1987}=3\)
tìm x,y,z biết
\(\frac{\text{x-1986 - 1987}}{1985}+\frac{\text{x- 1985 - 1987}}{1986}+\frac{\text{x-1985 - 1986}}{1987}=3\)
nhanh mk tick
\(\frac{x-1986-1987}{1985}+\frac{x-1985-1987}{1986}+\frac{x-1985-1986}{1987}=3\)
=> \(\left(\frac{x-1986-1987}{1985}-1\right)+\left(\frac{x-1985-1987}{1986}-1\right)+\left(\frac{x-1985-1986}{1987}-1\right)=3-3\)
=> \(\frac{x-1985-1986-1987}{1985}+\frac{x-1985-1986-1987}{1986}+\frac{x-1985-1986-1987}{1987}=0\)
=> \(\left(x-1985-1986-1987\right).\left(\frac{1}{1985}+\frac{1}{1986}+\frac{1}{1987}\right)=0\)
=> \(\left(x-5958\right).\left(\frac{1}{1985}+\frac{1}{1986}+\frac{1}{1987}\right)=0\)
Mà \(\frac{1}{1985}+\frac{1}{1986}+\frac{1}{1987}\ne0\)
=> x - 5958 = 0
=> x = 5958
Cho A=\(\frac{1985\text{×}1987-1}{1980+1985\text{×}1986}\)
Hãy so sánh A với 1
\(A=\left(1985\cdot1987-1\right):\left(1980+1985\cdot1986\right)\)
\(A=3944194\div3944190\)
ko chia hết nên sẽ bằng 1,4 lớn hơn 1
\(\Rightarrow A>1\)
1985x1987-1/1980+1985x1986=1985x1986+1985-1/1980+1985x1986
=1985x1986+1984/1980+1985x1986.Vì 1985x1986+1984>1980+1985x1986
suy ra 1985x1987-1/1980+1985x1986>1
Ta so sánh 1985 x 1987-1 và 1980 + 1985 x 1986
Ta có : 1985 x 1987 -1=1985 x ( 1986 +1) -1
=1985 x 1986 +1985 -1
=1985 x 1986 +1984
Mà 1985 x 1986 +1984 > 1980 + 1985 x 1986
Suy ra 1985 x 1987-1 > 1980 + 1985 x 1986
Suy ra \(\frac{1985x1987-1}{1980+1985x1986}\)>1
Dựa vào tính chất băc cầu hãy so sánh:
a) \(\frac{-37\ }{946}\) và \(\frac{-1}{-8}\)
b) \(\frac{-1987}{-1986}\) và \(\frac{-1984}{-1985}\)
Let a,b,c,d,e are integers satisfying the following expression:
\(\frac{501}{2015}\)=\(\frac{1}{a+\frac{1}{b+\frac{1}{c+\frac{1}{d+\frac{1}{e}}}}}\)
Find the value of a+b+c+d+e
Toán tiếng anh,giải giúp mik
Ta có: 2015/501=4+11/501 =>a=4
501/11=45+6/11 =>b=45
11/6=3+2/3 =>c=3
3/2=1+1/2 =>d=1
2/1=2 =>e=2
Vậy a=4 :b=45 :c=3 :d=1: e=2
Chúc bạn học tốt . Để dễ hiểu bạn hãy tham hảo đề toán giải máytính cầm tay
Each letter stands for a different digit (0,1,2,...,9) and \(P+\frac{1}{q+\frac{1}{r}}=\frac{35}{9}\)
Which of the following value is equal to p x q x r?
là 24 bạn nhé! tks
What is the largest integer n such that there is a multiple of 4 less than n2 but greater than n2+\(\frac{2016}{n^2}\)?
Bài 11:
Tính \(\frac{\left(1986^2-1992\right)\left(1986^2+3972-3\right).1987}{1983.1985.1988.1989}\)
Bài 12: Đặt \(a+b+c=2p\). CMR:
\(\frac{1}{p-a}+\frac{1}{p-b}+\frac{1}{p-c}-\frac{1}{p}=\frac{abc}{p\left(p-a\right)\left(p-b\right)\left(p-c\right)}\)
Bài 11 : ta có :
\(\frac{\left(1986^2-1992\right)\left(1986^2+3972-3\right)1987}{1983.1985.1988.1989}\)
\(=\frac{\left(1986^2-3.1986+2.1986-6\right)\left(1986^2+2.1986+1-4\right)1987}{1983.1985.1988.1989}\)
\(=\frac{\left(1986-3\right)\left(1986+2\right)\left[\left(1986+1\right)^2-2^2\right]1987}{1983.1985.1988.1989}\)
\(=\frac{1983.1988\left(1987-2\right)\left(1987+2\right)1987}{1983.1988.1985.1989}\)
\(=\frac{1983.1985.1988.1989.1987}{1983.1985.1988.1989}=1987\)