$\color{blue}{Tính B = 1.2.3 + 2.3.4 + … + (n – 1)n(n + 1)}$ $\color{red}{ai lm hộ mik ik}$

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1. B=1.2.3+2.3.4+.........+(n−1)n(n+1)

   Ta có4B=1.2.3.4+2.3.4.4+……..+(n−1)n(n+1).4

   =>4B=(4−0).1.2.3+(5−1).2.3.4+.........+[(n+2)−(n−2)](n−1)n(n+1)

   =>4B=1.2.3.4−0.1.2.3+2.3.4.5−1.2.3.4+…….+(n−1)n(n+1)(n+2)(n+3)−(n−2)(n−1)n(n+1)

   =>4B=(n−1)n(n+1)(n+2)

   =>B= (n−1)n(n+1)(n+2)/4`

    

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2.  

   Giải thích các bước giải:

   `B=1.2.3+2.3.4+.........+(n−1)n(n+1)`

   `⇔4B=1.2.3.4+2.3.4.4+........+(n−1)n(n+1).4`

   `⇔4B=(4−0).1.2.3+(5−1).2.3.4+.........+[(n+2)−(n−2)](n−1)n(n+1)`

   `⇔4B=1.2.3.4−0.1.2.3+2.3.4.5−1.2.3.4+.......+(n−1)n(n+1)(n+2)(n+3)−(n−2)(n−1)n(n+1)`

   `⇔4B=(n−1)n(n+1)(n+2)`

   `⇔B=`   `(n−1)n(n+1)(n+2)/4`

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