Ta có: \(A=1\cdot3\cdot3+3\cdot5\cdot5+\cdots+97\cdot99\cdot99\)

\(=1\cdot3^2+3\cdot5^2+\cdots+97\cdot99^2\)

\(=3^2\left(3-2\right)+5^2\left(5-2\right)+\cdots+99^2\left(99-2\right)\)

\(=\left(3^3+5^3+\cdots+99^3\right)-2\left(3^2+5^2+\cdots+99^2\right)\)

\(=\left(1^3+3^3+5^3+\cdots+99^3\right)-2\left(1^2+3^2+5^2+\cdots+99^2\right)+1\)

Đặt \(B=1^3+3^3+\cdots+99^3\)

\(=\left(1^3+2^3+\cdots+100^3\right)-\left(2^3+4^3+\cdots+100^3\right)\)

\(=\left(1+2+\cdots+100\right)^2-2^3\left(1^3+2^3+\cdots+50^3\right)\)

\(=\left(100\cdot\frac{101}{2}\right)^2-8\cdot\left(1+2+\cdots+50\right)^2\)

\(=\left(50\cdot101\right)^2-8\cdot\left(50\cdot\frac{51}{2}\right)^2\)

\(=5050^2-8\cdot1275^2=12497500\)

Đặt \(C=1^2+3^2+5^2+\cdots+99^2\)

\(=\left(1^2+2^2+\cdots+100^2\right)-\left(2^2+4^2+\cdots+100^2\right)\)

\(=\frac{100\left(100+1\right)\left(2\cdot100+1\right)}{6}-2^2\left(1^2+2^2+\cdots+50^2\right)\)

\(=\frac{100\cdot101\cdot201}{6}-4\cdot\frac{50\left(50+1\right)\left(2\cdot50+1\right)}{6}\)

\(=50\cdot101\cdot67-\frac23\cdot50\cdot51\cdot101=338350-171700=166650\)

Ta có: A=B-2C+1

=12497500-2*166650+1

=12164201

Ta có: \(A=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.....\frac{99^2}{98.100}\)

\(A=\frac{\left(2.3.4.5.....99\right).\left(2.3.4.5.....99\right)}{\left(1.2.3.4.....98\right).\left(3.4.5.6.....100\right)}\)

\(A=\frac{99.2}{100}=\frac{99}{50}\)

Học tốt!!!!

A = (2.3.4. .... .999/1.2.3. .... .998) . (2.3.4. .... .999/3.4.5. ..... .1000)

    = 999. 2/1000

    = 999/500

Tk mk nha

\(A=\dfrac{2^2}{1\cdot3}\cdot\dfrac{3^2}{2\cdot4}\cdot\dfrac{4^2}{3\cdot5}\cdot...\cdot\dfrac{999^2}{998\cdot1000}\\ =\dfrac{2^2\cdot3^2\cdot4^2\cdot...\cdot999^2}{1\cdot3\cdot2\cdot4\cdot3\cdot5\cdot...\cdot998\cdot1000}\\ =\dfrac{\left(2\cdot3\cdot4\cdot...\cdot999\right)\cdot\left(2\cdot3\cdot4\cdot...\cdot999\right)}{\left(1\cdot2\cdot3\cdot...\cdot998\right)\cdot\left(3\cdot4\cdot5\cdot...\cdot1000\right)}\\ =\dfrac{2\cdot3\cdot4\cdot...\cdot999}{1\cdot2\cdot3\cdot...\cdot998}\cdot\dfrac{2\cdot3\cdot4\cdot...\cdot999}{3\cdot4\cdot5\cdot...\cdot1000}\\ =999\cdot\dfrac{1}{500}\\ =\dfrac{999}{500}\)

A=1²/1.2 . 2²/2.3 . 3²/3.4 . 4²/4.5 . 5²/5.6

⇒1.1/1.2 . 2.2/2.3 . 3.3/3.4 . 4.4/4.5 . 5.5/5.6

⇒1.2.3.4.5/1.2.3.4.5 . 1.2.3.4.5/2.3.4.5.6

⇒1 . 1/6 =1/6.

Vậy A=1/6

B=2²/1.3 . 3²/2.4 . 4²/3.5 . 5²/4.6

⇒2.2/1.3 . 3.3/2.4 . 4.4/3.5 . 5.5/4.6

⇒2.2.3.3.4.4.5.5/1.3.2.4.3.5.4.6 =48.

Vậy B=48.