\(C=\frac{5}{2}\cdot\frac{7}{5}\cdot\frac{9}{7}\cdot\frac{11}{9}\cdot...\cdot\frac{2017}{2015}\cdot\frac{2019}{2017}=\frac{2019}{2}\)

\(D=\left(1-\frac{1}{\frac{2\cdot3}{2}}\right)\cdot\left(1-\frac{1}{\frac{3\cdot4}{2}}\right)\cdot\left(1-\frac{1}{\frac{4\cdot5}{2}}\right)\cdot\left(1-\frac{1}{\frac{5\cdot6}{2}}\right)\cdot...\cdot\left(1-\frac{1}{\frac{39\cdot40}{2}}\right)\)

\(=\left(1-\frac{2}{2\cdot3}\right)\cdot\left(1-\frac{2}{3\cdot4}\right)\cdot\left(1-\frac{2}{4\cdot5}\right)\cdot\left(1-\frac{2}{5\cdot6}\right)\cdot...\cdot\left(1-\frac{2}{39\cdot40}\right)\cdot\)

Nhận xét: \(1-\frac{2}{n\left(n+1\right)}=\frac{n\left(n+1\right)-2}{n\left(n+1\right)}=\frac{n^2+n-2}{n\left(n+1\right)}=\frac{\left(n+2\right)\left(n-1\right)}{n\left(n+1\right)}\)nên:

\(D=\frac{4\cdot1}{2\cdot3}\cdot\frac{5\cdot2}{3\cdot4}\cdot\frac{6\cdot3}{4\cdot5}\cdot\frac{7\cdot4}{5\cdot6}\cdot\frac{8\cdot5}{6\cdot7}\cdot...\cdot\frac{41\cdot38}{39\cdot40}=\)

\(D=\frac{4\cdot5\cdot6\cdot7\cdot...\cdot41\times1\cdot2\cdot3\cdot4\cdot...\cdot38}{2\cdot3\cdot4\cdot5\cdot...\cdot39\times3\cdot4\cdot5\cdot6\cdot..\cdot40}=\frac{1}{39}\cdot\frac{41}{3}=\frac{41}{117}\)

1> 3x(x-2)-2x(2x-1)=(1-x)(1+x)

⇔\(3x^2\)-6x-\(4x^2\)+2x=1-\(x^2\)

⇔-1\(x^2\) - 4x= 1- \(x^2\)

⇔ -1\(x^2\) -4x+ \(x^2\) = 1

⇔-4x=1

⇔ x = \(\dfrac{-1}{4}\)

\(b,\)\(B=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(\Rightarrow B=1.\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(\Rightarrow B=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(\Rightarrow B=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(\Rightarrow B=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(\Rightarrow B=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(\Rightarrow B=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(\Rightarrow B=\left(2^{32}-1\right)\left(2^{32}+1\right)-2^{64}\)

\(\Rightarrow B=2^{64}-1-2^{64}=-1\)

a) Đặt \(A=\left(\frac{1}{2}+1\right).\left(\frac{1}{4}+1\right).\left(\frac{1}{16}+1\right)...\left(1+\frac{1}{2^{2n}}\right)\)

Rút gọn:  \(A=\frac{2+1}{2}.\frac{4+1}{4}.\frac{16+1}{16}...\frac{2^{2.n}+1}{2^{2.n}}=\frac{2^{2.0}+1}{2^{2.0}}.\frac{2^{2.1}+1}{2^{2.1}}.\frac{2^{2.2}+1}{2^{2.2}}...\frac{2^{2.n}+1}{2^{2.n}}\)

\(\Rightarrow A=\frac{\left(2^{2.0}+1\right).\left(2^{2.1}+1\right).\left(2^{2.2}+1\right)...\left(2^{2.n}+1\right)}{2^{2.0}.2^{2.1}.2^{2.2}...2^{2.n}}.\)

b) Đặt \(B=\left(2+1\right).\left(2^2+1\right).\left(2^4+1\right).\left(2^8+1\right).\left(2^{16}+1\right).\left(2^{32}+1\right)-2^{64}\)

\(\Leftrightarrow B=\left(2-1\right).\left(2+1\right).\left(2^2+1\right)...\left(2^{32}+1\right)-2^{64}=\left(2^2-1\right).\left(2^2+1\right)...\left(2^{32}+1\right)-2^{64}\)

\(\Leftrightarrow B=\left(2^4-1\right).\left(2^4+1\right).\left(2^8+1\right)...\left(2^{32}+1\right)-2^{64}=\left(2^8-1\right).\left(2^8+1\right)...\left(2^{32}+1\right)-2^{64}\)

\(\Leftrightarrow B=\left(2^{16}-1\right).\left(2^{16}+1\right).\left(2^{32}+1\right)-2^{64}=\left(2^{32}-1\right).\left(2^{32}+1\right)-2^{64}\)

\(\Leftrightarrow B=2^{64}-1-2^{64}=-1\)Vậy B =-1.

1,(x+2)(x+5)(x+3)(x+4)-24=(x²+7x+10)(x²+7x+12)-24

Đặt x²+7x+10= t ta có t(t+2)-24=t²+2t-24=(t-4)(t+6)

hay (x²+7x+6)(x²+7x+16)

2,x(x+10)(x+4)(x+6)+128=(x²+10x)(x²+10x+24)+128

Đặt x²+10x=t ta có t(t+24)+128=t²+24t+128=(t+8)(t+16)

hay (x²+10x+8)(x²+10x+16)

3,(x+2)(x-7)(x+3)(x-8)-144=(x^2-5x-14)(x²-5x-24)-144

Đặt x²-5x-14=t ta có t(t-10)-144=t²-10t-144=(t-18)(t+8)

Hay (x²-5x-32)(x²-5x-6)=(x²-5x-32)(x+1)(x-6)

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`#3107.101107`

`-3^2 + {-54 \div [-2^8 + 7] * (-2)^2}`

`= -9 + [-54 \div (-256 + 7) * 4]`

`= -9 + [-54 \div (-249) * 4]`

`= -9 + (18/83 * 4)`

`= -9 + 72/83`

`= -675/83`

______

`31 * (-18) + 31 * (-81) - 31`

`= 31 * (-18 - 81 - 1)`

`= 31 * (-100)`

`= -3100`

___

`(-12) * 47 + (-12) * 52 + (-12)`

`= (-12) * (47 + 52 + 1)`

`= (-12) * 100`

`= -1200`

___

`13 * (23 + 22) - 3 * (17 + 28)`

`= 13 * 45 - 3 * 45`

`= 45 * (13 - 3)`

`= 45 * 10`

`= 450`

____

`-48 + 48 * (-78) + 48 * (-21)`

`= 48 * (-1 - 78 - 21)`

`= 48 * (-100)`

`= -4800`

sai đề bn ơi

Sai phần tử rùi pn ơi

= (1/2).(2/3).(4/5).(5/6)......(2016/2017).(2017/2018)

=1.2.3.4.5......2016.2017/2.3.4.5.....2017.2018

=1/2018

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\cdot\cdot\cdot\cdot\cdot\left(1-\frac{1}{2017}\right)\left(1-\frac{1}{2018}\right)\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\cdot\cdot\cdot\cdot\frac{2016}{2017}\cdot\frac{2017}{2018}\)

\(=\frac{1\cdot2\cdot3\cdot\cdot\cdot\cdot\cdot2016\cdot2017}{2\cdot3\cdot4\cdot\cdot\cdot\cdot2017\cdot2018}\)

\(=\frac{1}{2018}\)