\(C=1.2.3+2.3.4+...+48.49.50\)

\(\Rightarrow4C=1.2.3.4+2.3.4.4+...+48.49.50.4\)

\(=1.2.3.4+2.3.4.\left(5-1\right)+...+48.49.50.\left(51-47\right)\)

\(=1.2.3.4+2.3.4.5-1.2.3.4+...+48.49.50.51-47.48.49.50\)

\(=48.49.50.51\)

\(\Rightarrow C=\frac{48.49.50.51}{4}=1499400\)

đặt A = 1.2.3 + 2.3.4 + 3.4.5 + ... + 48.49.50

4A = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + ...+ 48.49.50.4

4A = 1.2.3.4 + 2.3.4.(5-1) + 3.4.5.(6-2) + ... + 48.49.50.(51-47)

4A = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + ... + 48.49.50.51 - 47.48.49.50

4A = 48.49.50.51

A = \(\frac{48.49.50.51}{4}\)

A = 1499400

a) A = 1.( 2 + 1 ) + 2.( 3 + 1 ) + 3.( 4 + 1 ) + ...+ 98.( 99 + 1 )

A = 1.2 + 1 + 2.3 + 2 + 3.4 + 3 + ... + 98.99 + 98

A = ( 1.2 + 2.3 + 3.4 + ... + 98.99 ) + ( 1 + 2 + 3 + 4 + ... + 98 )

Dat B = 1.2 + 2.3 + 3.4 + ...+ 98.99

      C = 1 + 2 + 3 + 4 + ... + 98

=> 3B = 1.2.3 + 2.3.3 + 3.4.3 + ...+ 98.99.3

          = 1.2.3 + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + ....+ 98.99.( 100 - 97 )

         = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 98.99.100 - 97.98.99

=> B = ( 98.99.100 ) : 3 = 323400

=> C = 1 + 2 + 3 + ... 98

     C = 98 + 97 + ...+ 3 + 2 + 1

Tu lam tiep nha

a)

A= 1.2 +1.2.3+2+3.4+3+......98.99+98

A=(1.2+2.3+3.4+........98.99)+(1+2+3+4+...98)

Đặt A=1.2.3+2.3.4+3.4.5+........+48.49.50

     4A=1.2.3.4+2.3.4.4+..........+48.49.50.4

         =1.2.3.4+2.3.4.(5-1)+.........+48.49.50.(51-47)

         =1.2.3.4+2.3.4.5-1.2.3.4+...........+48.49.50.51-47.48.49.50

         =48.49.50.51

         =5997600

       A=1499400

Vậy A=1499400

Đặt \(A=1\cdot2\cdot3+2\cdot3\cdot4+........+48\cdot49\cdot50\)

\(\Rightarrow4A=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot4+......+48\cdot49\cdot50\cdot4\)

\(=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot\left(5-1\right)+..........+48\cdot49\cdot50\cdot\left(51-47\right)\)

\(=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+......+48\cdot49\cdot50\cdot51-47\cdot48\cdot49\cdot50\)

\(=48\cdot49\cdot50\cdot51\)

\(\Rightarrow A=\frac{48\cdot49\cdot50\cdot51}{4}\)

Ai hack nick mình thì trả lại đi !!!

nick : 

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Ta có: \(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{8.9.10}\right)x=\frac{23}{45}\)

\(\Rightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)x=\frac{23}{45}\)

\(\Rightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{9.10}\right)x=\frac{23}{45}\)

\(\Rightarrow\frac{1}{2}\left(\frac{1}{2}-\frac{1}{90}\right)x=\frac{23}{45}\)

\(\Rightarrow\frac{11}{45}x=\frac{23}{45}\)

\(\Rightarrow x=\frac{23}{45}:\frac{11}{45}\)

\(\Rightarrow x=\frac{23}{11}\)

Đặt A=\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{8.9.10}\)

    2A=\(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{8.9.10}\)

    2A=\(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}\) \(+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{8.9}-\frac{1}{9.10}\)

    2A=\(\frac{1}{1.2}-\frac{1}{9.10}\)

    2A=\(\frac{22}{45}\)

      A=\(\frac{22}{45}\div2\)

      A=\(\frac{11}{45}\)

\(\Rightarrow\frac{11}{45}.x=\frac{23}{45}\)

             \(x=\frac{23}{45}\div\frac{11}{45}=\frac{23}{11}\)

Vậy x=\(\frac{23}{11}\)

B = 49.(49 + 1).(2 . 49 + 1) / 6 = 40425

C = 4.(1² + 2² + … + 24² ) = 4.24.(24 + 1)(2.24 + 1) / 6 = 19600

\(A=1.2.3+2.3.4+3.4.5+...+48.49.50\)

\(4A=1.2.3.4+2.3.4.4+3.4.5.4+...+48.49.50.4\)

\(4A=1.2.3.\left(4-0\right)+2.3.4.\left(5-1\right)+...+48.49.50.\left(51-47\right)\)

\(4A=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+...+48.49.50.51-48.48.49.50\)

\(4A=48.49.50.51\)

\(A=\dfrac{48.49.50.51}{4}=1499400\)

A=1499400 nhe ban !

4A=4.[1.2.3 + 2.3.4 + 3.4.5 + 4.5.6 + . . . . . . + 48.49.50]
4A=1.2.3.4 +2.3.4.4 +3.4.5.4 +4.5.6.4 +.........+48.49.50.4
4A=1.2.3.4 +2.3.4.(5-1) + 3.4.5.(6-2) +4.5.6(7-3)+....+ 48.49.50(51-47)
4A=1.2.3.4 +2.3.4.5 --1.2.3.4 + 3.4.5.6--2.3.4.5 + 4.5.6.7-3.4.5.6+....+ 48.49.50.51--47.48.49.50
4A =48.49.50.51
A=(48.49.50.51)/4