When n=n+ 1, an item [2 (n+ 1)] 3 is added to the left.
=(2n+2)^3
=8n^3+24n^2+24n+8…………………………………( 1)
Right = 2 (n+ 1) 2x (n+2) 2
Added 2 (n+1) 2x (n+2) 2-2n2x (n+1) 2.
=2[(n+ 1)^2x(n+2)^2-n^2x(n+ 1)^2]
=2(n^2+2n+ 1)[(n^2+4n+4)-n^2]
=2(n^2+2n+ 1)(4n+4)
=2(4n^3+8n^2+4n+4n^2+8n+4)
=2(4n^3+ 12n^2+ 12n+4)
=8n^3+24n^2+24n+8…………………………………(2)
( 1)=(2)
Established.
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