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Sum from r=1 to n (3r+1) = n/2(3n+5)

Prove true for n=1:

3*1+1=4 | 1/2(3*1+5)=4

Assume true for n=k:

k/2(3k+5)

Prove true for n=(k+1):

k/2(3k+5) + (3(k+1)+1) | 1/2(k+1)(3(k+1)+5)

k/2(3k+5) + (3k+3+1) | 1/2(k+1)(3k+3+5)

k/2(3k+5) + (3k+4) | 1/2(k+1)(3k+8)

now what? I can't see what factors I can take out of either to make them the same... any ideas?

EDIT: nevermind:

1/2(3k^2+5k+2(3k+4) | 1/2(k+1)(3k+8)

1/2(3k^2+11k+8) | 1/2(k+1)(3k+8)

1/2(k+1)(3k+8) | 1/2(k+1)(3k+8)

Same, therefore proved by induction.

:D

Prove true for n=1:

3*1+1=4 | 1/2(3*1+5)=4

Assume true for n=k:

k/2(3k+5)

Prove true for n=(k+1):

k/2(3k+5) + (3(k+1)+1) | 1/2(k+1)(3(k+1)+5)

k/2(3k+5) + (3k+3+1) | 1/2(k+1)(3k+3+5)

k/2(3k+5) + (3k+4) | 1/2(k+1)(3k+8)

now what? I can't see what factors I can take out of either to make them the same... any ideas?

EDIT: nevermind:

1/2(3k^2+5k+2(3k+4) | 1/2(k+1)(3k+8)

1/2(3k^2+11k+8) | 1/2(k+1)(3k+8)

1/2(k+1)(3k+8) | 1/2(k+1)(3k+8)

Same, therefore proved by induction.

:D

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