induction proof manipulation problem











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starting with the LHS, how do you show



$(k/30)(k+1)(6k^3+9k^2+k-1)+(k+1)^4$= $(k+1)/30(k+2)(6(k+1)^3+9(k+1)^2+(k+1)-1$



as you can probably tell its part of my induction proof but i cant show this how is it done? thanks



Sorry edit its -1 on the end










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  • the main thing would be NOT to factor the quintic $ 6k^5 + 15k^4 + 10k^3 - k$ Since leaving off the denominator , add to that $30 (k+1)^4$
    – Will Jagy
    Nov 20 at 2:30










  • yep, that works
    – Will Jagy
    Nov 20 at 2:37















up vote
1
down vote

favorite












starting with the LHS, how do you show



$(k/30)(k+1)(6k^3+9k^2+k-1)+(k+1)^4$= $(k+1)/30(k+2)(6(k+1)^3+9(k+1)^2+(k+1)-1$



as you can probably tell its part of my induction proof but i cant show this how is it done? thanks



Sorry edit its -1 on the end










share|cite|improve this question






















  • the main thing would be NOT to factor the quintic $ 6k^5 + 15k^4 + 10k^3 - k$ Since leaving off the denominator , add to that $30 (k+1)^4$
    – Will Jagy
    Nov 20 at 2:30










  • yep, that works
    – Will Jagy
    Nov 20 at 2:37













up vote
1
down vote

favorite









up vote
1
down vote

favorite











starting with the LHS, how do you show



$(k/30)(k+1)(6k^3+9k^2+k-1)+(k+1)^4$= $(k+1)/30(k+2)(6(k+1)^3+9(k+1)^2+(k+1)-1$



as you can probably tell its part of my induction proof but i cant show this how is it done? thanks



Sorry edit its -1 on the end










share|cite|improve this question













starting with the LHS, how do you show



$(k/30)(k+1)(6k^3+9k^2+k-1)+(k+1)^4$= $(k+1)/30(k+2)(6(k+1)^3+9(k+1)^2+(k+1)-1$



as you can probably tell its part of my induction proof but i cant show this how is it done? thanks



Sorry edit its -1 on the end







proof-writing






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 20 at 1:55









hitherematey

577




577












  • the main thing would be NOT to factor the quintic $ 6k^5 + 15k^4 + 10k^3 - k$ Since leaving off the denominator , add to that $30 (k+1)^4$
    – Will Jagy
    Nov 20 at 2:30










  • yep, that works
    – Will Jagy
    Nov 20 at 2:37


















  • the main thing would be NOT to factor the quintic $ 6k^5 + 15k^4 + 10k^3 - k$ Since leaving off the denominator , add to that $30 (k+1)^4$
    – Will Jagy
    Nov 20 at 2:30










  • yep, that works
    – Will Jagy
    Nov 20 at 2:37
















the main thing would be NOT to factor the quintic $ 6k^5 + 15k^4 + 10k^3 - k$ Since leaving off the denominator , add to that $30 (k+1)^4$
– Will Jagy
Nov 20 at 2:30




the main thing would be NOT to factor the quintic $ 6k^5 + 15k^4 + 10k^3 - k$ Since leaving off the denominator , add to that $30 (k+1)^4$
– Will Jagy
Nov 20 at 2:30












yep, that works
– Will Jagy
Nov 20 at 2:37




yep, that works
– Will Jagy
Nov 20 at 2:37















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