Transform term for induction proofCould you help me to mathematically show that these two terms are the same (they are). This is the last (but probably the most important :( ) step of an induction proof. F i r s t : ( n + 1 ) ( n + 2 ) ( 2 ( n + 1 ) + 7 ) 6 S e c o n d : n ( n + 1 ) ( 2 n + 7 ) + 6 ( n + 1 ) ( n + 3 ) 6 Thank you! :)

Question

Transform term for induction proofCould you help me to mathematically show that these two terms are the same (they are). This is the last (but probably the most important :( ) step of an induction proof.  F  i  r  s  t  :            (      n      +      1      )      (      n      +      2      )      (      2      (      n      +      1      )      +      7      )        6    S  e  c  o  n  d  :            n      (      n      +      1      )      (      2      n      +      7      )      +      6      (      n      +      1      )      (      n      +      3      )        6  Thank you! :)

Gracelyn Paul · Accepted Answer

Guide:Compare the common factors of the two terms. You can quickly remove             n      +      1        6  Hence you just have to prove that  (  n  +  2  )  (  2  (  n  +  1  )  +  7  )  =  n  (  2  (  n  +  1  )  +  7  )  +  6  (  n  +  3  )Try expanding both sides and check that they are equal.

Dulce Cantrell · Accepted Answer

A (hopefully) more elegant variant:Once you&#039;ve factored out                     n        +        1            6      , there remains  n  (  2  n  +  7  )  +  6  (  n  +  3  )  =  n            (        2  (  n  +  3  )  +  1            )        +  6  (  n  +  3  )  =      2    (    n    +    3          )      2        +    n    (  n  +  2  )            (        2  (  n  +  1  )  +  7            )        =            (        (  n  +  3  )  −  1            )                  (        2  (  n  +  3  )  +  3            )        =  2  (  n  +  3      )    2    +  (  3  −  2  )  (  n  +  3  )  −  3  =      2    (    n    +    3          )      2        +    n    .

Transform term for induction proof Could you help me to mathematically show that these two terms are the same (they are). This is the last (but probably the most important :( ) step of an induction proof. First: ((n+1)(n+2)(2(n+1)+7))/(6) Second: (n(n+1)(2n+7)+6(n+1)(n+3))/(6) Thank you! :)

Answered question

Answer & Explanation

New Questions in Pre-Algebra