Đặt A = \(\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^2}+...+\dfrac{100}{3^{100}}\)

\(\Rightarrow3A=1+\dfrac{2}{3}+\dfrac{3}{3^2}+...+\dfrac{100}{3^{99}}\)

\(2A=3A-A=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{99}}-\dfrac{100}{3^{100}}\)Đặt B= \(1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{99}}\)

\(\Rightarrow3B=3+1+\dfrac{1}{3}+...+\dfrac{1}{3^{98}}\)

\(2B=3B-B=3-\dfrac{1}{3^{99}}\)

Nhận xét : 2B < 3 => B < \(\dfrac{3}{2}\)

=> \(B-\dfrac{100}{3^{100}}< \dfrac{3}{2}\) hay 2A < \(\dfrac{3}{2}\)

=> Đpcm

***tik mik nhé***

\(x^2+4x+4=\left(x+2\right)^2\)

\(4x^2-4x+1=\left(2x-1\right)^2\)

\(4x^2+12x+9=\left(2x+3\right)^2\)

\(9x^2+30x+25=\left(3x+5\right)^2\)

\(4x^2-20x+25=\left(2x+5\right)^2\)

tik mik nha

bài này sai đề bạn ơi

1.

a) \(\left(a+b+c\right)^2=\left[\left(a+b\right)+c\right]^2\)

\(=\left(a+b\right)^2+2\left(a+b\right)c+c^2\)

\(=a^2+b^2+c^2+2ab+2bc+2ac\)

b)\(\left(a+b-c\right)^2=\left[\left(a+b\right)-c\right]^2\)

\(=\left(a+b\right)^2-2\left(a+b\right)c+c^2\)

\(=a^2+b^2+c^2+2ab-2ac-2bc\)

c)\(\left(a-b+c\right)^2=\left[\left(a-b\right)+c\right]^2\)

\(=\left(a-b\right)^2+2\left(a-b\right)c+c^2\)

\(a^2+b^2+c^2+2ac+2bc-2ab\)

d)\(\left(a-b-c\right)^2=\left[a-\left(b+c\right)\right]^2\)

\(=a^2-2a\left(b+c\right)+\left(b+c\right)^2\)

\(=a^2+b^2+c^2-2ab-2ac+2bc\)

nhớ tik mik nha

1. \(x^3+9x^2+27x+27=\left(x+3\right)^3\)

2.\(8x^6-27y^3=\left(2x\right)^3-\left(3y\right)^3=\left(2x-3y\right)\)

\(=\left(2x-3y\right)\left(8x^6+6xy+27y^3\right)\)

3.\(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3-y^3\right)\left(x^3+y^3\right)\)4.câu cuối là \(8b^3\)bạn nhé !!

tik mik nhé

Ta có \(\dfrac{2n+1}{6-n}=\dfrac{2n-12+13}{6-n}=\dfrac{2\left(n-6\right)+13}{6-n}\)

\(=-2+\dfrac{13}{6-n}\)

để \(2n+1⋮6-n\Rightarrow\dfrac{2n+1}{6-n}\in N\)

hay \(6-n\inƯ\left(13\right)\)

nên \(6-n\in\left(1;13\right)\)

ta có bảng

vậy giá trị n thỏa mãn là 5 ( mik chưa xét đên nghiệm âm ) .

tik mik nhé

câu 1a sai đề bạn ơi

1 . enjoyment.

2. arrival.

3. youth.

tik mik nha

What color ; what time

tik mik nhes !!!