Bài 6: Lũy thừa của một số hữu tỉ (tiếp theo...)

Ta có:

\(\dfrac{-11}{3^7.7^3}=\dfrac{-11}{\dfrac{3^7.7^4.1}{7}}=-\dfrac{77}{3^7.7^4}=\dfrac{-78+1}{3^7.7^4}=\dfrac{-78}{3^7.7^4}+\dfrac{1}{3^7.7^4}\)

Do \(3^7.7^4>3^4.7^4\)

\(\text{⇒}\dfrac{78}{3^7.7^4}< \dfrac{78}{3^4.7^4}\text{⇒}\dfrac{-78}{3^7.7^4}>\dfrac{-78}{3^4.7^4}\text{⇒}\dfrac{-78}{3^7.7^4}+\dfrac{1}{3^7.7^4}>\dfrac{-78}{3^4.7^4}\text{⇒}\dfrac{-11}{3^7.7^3}>\dfrac{-78}{3^4.7^4}\)

Lời giải:

$3^{n+2}-2^{n+2}+3^n-2^n=9.3^n-4.2^n+3^n-2^n$

$=(9.3^n+3^n)-(4.2^n+2^n)=10.3^n-5.2^n$

$=10.3^n-10.2^{n-1}=10(3^n-2^{n-1})\vdots 10$ với mọi $n\in\mathbb{N}^*$

Tham Khao

\(1^2+2^2+3^2+...+100^2=1.\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+100\left(101-1\right)=1.2-1+2.3-2+3.4-4+...+100.101-100=\left(1.2+2.3+3.4+...+100.101\right)-\left(1+2+3+...+100\right)=\dfrac{3\left(1.2+2.3+3.4+...+3.100.101\right)}{3}-\left(1+2+3+...+100\right)=\dfrac{1.2.3+2.3.\left(4-1\right)+3.4\left(5-2\right)+...+100.101\left(102-99\right)}{3}-\dfrac{\left(100+1\right)\left(\dfrac{100-1}{1}+1\right)}{2}=\dfrac{1.2.3-1.2.3+2.3.4-2.3.4+...+-99.100.101+100.101.102}{3}-5050=\dfrac{100.101.102}{3}-5050=343400-5050=338350\)

c)\(7^{2n}+7^{2n+2}=2450\)

⇒\(7^{2n}+7^{2n}.7^2=2450\)

⇒\(7^{2n}.50=2450\)

⇒\(7^{2n}=49\)\(=7^2\)

⇒2n=2

⇒n=1

a)\(\left(-\dfrac{1}{5}\right)^n=-\dfrac{1}{125}\)                   b)\(\left(-\dfrac{2}{11}\right)^m=\dfrac{4}{121}\)

\(\left(-\dfrac{1}{5}\right)^n=\left(-\dfrac{1}{5}\right)^3\)                    \(=\left(-\dfrac{2}{11}\right)^m=\left(-\dfrac{2}{11}\right)^2\)

⇒n=3                                          ⇒m=2

\(3^{21}=3^{20}.3=9^{10}.3\)

\(2^{31}=2^{30}.2=8^{10}.2\)

Do \(9^{10}>8^{10},3>2\)

\(\Rightarrow9^{10}.3>8^{10}.2\Rightarrow3^{21}>2^{31}\)

\(3^{21}=3^{20}\cdot3\)

\(2^{31}=2^{30}\cdot2\)

mà \(3^{20}>2^{30}\)

nên \(3^{21}>2^{31}\)

\(\left(-1\right)^{2n}+\left(-1\right)^{2n+1}=1^n+1^n.\left(-1\right)=1^n-1^n=0\)

Đề bài ???

\(2.16>2^n>4\)

\(\Rightarrow2^5>2^n>2^2\)

\(\Rightarrow n\in\left\{3;4\right\}\)

2.16 là 2,16 hay 2 x 16 nhỉ

có 5 nha

quy đồng -5/6 và -1/2 có mẫu chung là 18 rồi đếm thôi

mong like cho

Gọi tử số là a

Theo đề, ta có: \(\dfrac{-5}{6}< \dfrac{a}{18}< \dfrac{-1}{2}\)

\(\Leftrightarrow-15< a< -9\)

Vậy: Có 5 phân số