ChoA=(10^n+10^n-1+10^n-2...+10+1)×(10^n+1 +3)+11la so chinh phuong
Rút gọn biểu thức:
a) 10^n+1-6*10^n
b) 90*10^n-10^n-2+10^n+1
c) 2,5 *56^n-3
a) \(10^n+1-6\cdot10^n=\left(1-6\right)10^n+1=-5\cdot10^n+1\)
b) \(90\cdot10^n-10^2-2+10^n+1=\left(90-1+1\right)\cdot10^n-2+1=90\cdot10^n-1\)
c) \(2,5\cdot56^n-3=\frac{5}{2}\cdot56^n-3\)
So sánh 10^n/ 10^n+1 và 10^n+1/ 10^n+2
Giải:
Ta có:
\(\dfrac{10^n}{10^n+1}=\dfrac{10^n+1-1}{10^n+1}=1-\dfrac{1}{10^n+1}\)
\(\dfrac{10^n+1}{10^n+2}=\dfrac{10^n+2-1}{10^n+2}=1-\dfrac{1}{10^n+2}\)
Vì \(\dfrac{1}{10^n+1}>\dfrac{1}{10^n+2}\)
\(\Leftrightarrow-\dfrac{1}{10^n+1}< -\dfrac{1}{10^n+2}\)
\(\Leftrightarrow-\dfrac{1}{10^n+1}+1< -\dfrac{1}{10^n+2}+1\)
Hay \(1-\dfrac{1}{10^n+1}< 1-\dfrac{1}{10^n+2}\)
\(\Leftrightarrow\dfrac{10^n}{10^n+1}< \dfrac{10^n+1}{10^n+2}\)
Vậy ...
So sánh:
a)A=1010+4/10^10-1 và B=1010+3/1010-2
b)A=10n/10n+1 và B=10n+1/10n+2
(Ghi đầy đủ cách giải)
so sánh:
a) n+1/n+2 với n/n+3
b) 10^11-1/10^12-1 với 10^10+1/10^11+1
a) Ta có
A = n / n+1 = 1-(1/n+1)
A = n+2 / n+3 = 1-(1/n+3)
Vì 1/n+1 > 1/n+3
=> n/n+1 < n+2/n+3
=> A<B
Tính
\(\frac{10^{n+2}}{10^n}-\frac{10^{n+1}}{10^{n+1}}=\)
bn vừa phải thôi đó Phạm Mai Chi
ko tl cho người ta thì thôi đi
Cho A=(10^n+10^n-1...+10+1)×(10^n+1 +3)+1la so cp
Chứng minh rằng với \(n\in N\) thì A là số chính phương biết:
\(A=\left(10^n+10^{n-1}....+10+1\right)\left(10^{n+1}+5\right)+1\)
Lời giải:
Xét:
$M=1+10+....+10^n$
$10M=10+10^2+....+10^{n+1}$
$10M-M=10^{n+1}-1$
$M=\frac{10^{n+1}-1}{9}$
$A=M.(10^{n+1}+5)+1=\frac{(10^{n+1}-1)(10^{n+1}+5)}{9}+1$
$=\frac{10^{2n+2}+4.10^{n+1}-5+9}{9}$
$=\frac{10^{2n+2}+4.10^{n+1}+4}{9}$
$=\frac{(10^{n+1}+2)^2}{9}$
$=\left(\frac{10^{n+1}+2}{3}\right)^2$
Ta thấy: $10^{n+1}+2\equiv 1^{n+1}+2=3\equiv 0\pmod 3$
Do đó: $\frac{10^{n+1}+2}{3}\in\mathbb{N}$
Suy ra $A$ là scp.
Rut gon:
a, 10n + 1 - 6 . 10n
b, 90 . 10n - 10n + 2 + 10n +1
a)10n+1-6.10n
=10n.10-6.10n
=10n(10-6)
=10n.4
b)90.10n-10n+2+10n+1
=90.10n-10n.100+10n+10
=10n(90-100+10)
=10n.0
=0
a, \(10^{n+1}-6.10^n\)
= \(10^n.10-6.10^n\)
=\(10^n.\left(10-6\right)\)
=\(10^n.4\)
b, \(90.10^n-10^{n+2}-10^{n+1}\)
= \(90.10^n-10^n.10^2-10^n.10\)
= \(10^n.\left(90-10^2-10\right)\)
= \(10^n.\left(-20\right)\)
nhớ k cho mik nha!!!!!!!!!!!!!