Rational Expression:n(n+1)(n+2)(n+3)

[From: ] [author: ] [Date: 12-10-17] [Hit: ]

[4n^4+ (1+4+8+12)n^3+(3+2+24+1+12+8)n^2+(6+3+2+…[4n^4+ 25n^3+50n^2+35n+6]/24-It is unclesr to me what the question actually is. Can you show the original question?......

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According to additional details, the equation at the very top is incorrect, making your second line correct. This is what you should get then:

n(n+1)(n+2)(n+3)/(2*3*4) + (n+1)(n+2)(n+3)/(2*3)

= n(n+1)(n+2)(n+3)/(2*3*4) + (n+1)(n+2)(n+3)*4/(2*3*4)

= (n(n+1)(n+2)(n+3) + 4(n+1)(n+2)(n+3)) / (2*3*4)

= (n+1)(n+2)(n+3) (n + 4) / 24

= (n² + 2n + n + 2) (n² + 4n + 3n + 12) / 24

= (n² + 3n + 2) (n² + 7n + 12) / 24

= (n² (n² + 7n + 12) + 3n (n² + 7n + 12) + 2 (n² + 7n + 12)) / 24

= (n⁴ + 7n³ + 12n² + 3n³ + 21n² + 36n + 2n² + 14n + 24) / 24

= (n⁴ + 10n³ + 35n² + 50n + 24) / 24

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if it is:
[n(n+1)(n+2)(n+3)]/(2*3) + [(n+1)(n+2)(n+3)]/(2*3*4) => can be factored as:

= [(n+1)(n+2)(n+3)]/(2*3)] [ n + 1/4]

= (n^3 + 6n^2 + 11n + 6)/6 * (4n + 1)/4

= 1/24 * (4n^4 + 25n^3 + 50n^2 + 35n + 6)

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n(n+1)(n+2)(n+3)/3! + (n+1)(n+2)(n+3)/4!
=4n(n+1)(n+2)(n+3)/4!+ (n+1)(n+2)(n+3)/4!
=(n+1)(n+2)(n+3)[4n+1)/4!
[4n^4+ (1+4+8+12)n^3+(3+2+24+1+12+8)n^2+(6+3+2+…
[4n^4+ 25n^3+50n^2+35n+6]/24

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It is unclesr to me what the question actually is.
Can you show the original question?

12

keywords: Rational,Expression,Rational Expression:n(n+1)(n+2)(n+3)