How does this seemingly-trivial simplification work?In a section on inductive proofs in the book Modelling Computing Systems: Mathematics for Computer Science (Muller, Struth) there is a simplification that is assumed to be trivial, but that I can't figure out.It occurs in this step: k ( k + 1 ) ( k + 2 ) 3 + ( k + 1 ) ( k + 2 ) = ? ( k + 1 ) ( k + 2 ) ( k + 3 ) 3 How does one get from the first expression to the second?

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How does this seemingly-trivial simplification work?In a section on inductive proofs in the book Modelling Computing Systems: Mathematics for Computer Science (Muller, Struth) there is a simplification that is assumed to be trivial, but that I can&#039;t figure out.It occurs in this step:            k      (      k      +      1      )      (      k      +      2      )        3    +  (  k  +  1  )  (  k  +  2  )                    =                    ?                        (      k      +      1      )      (      k      +      2      )      (      k      +      3      )        3  How does one get from the first expression to the second?

wasipewelr · Accepted Answer

k            (            k            +            1            )            (            k            +            2            )                    3                +        (        k        +        1        )        (        k        +        2        )                            =                                            k                        (            k            +            1            )            (            k            +            2            )            +                          3                        (            k            +            1            )            (            k            +            2            )                    3                                                  =                              (            k            +            1            )            (            k            +            2            )            (                          k                        +                          3                        )                    3

Riya Hansen · Accepted Answer

Hint:  (  k  +  1  )  (  k  +  2  )  =            3      ⋅      (      k      +      1      )      (      k      +      2      )        3    .Now combine the fractions and factor out   (  k  +  1  )  (  k  +  2  )

How does this seemingly-trivial simplification work? In a section on inductive proofs in the book M

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