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Question

Prove: 12+22+32+.........n2>n33

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Solution

Prove that 12+22+...+n2>n33,nN
Let P(n):12+22+.....+n2>n33,nN
For n=1
L.H.S=12=1
R.H.S=133=13
since 1>13
L.H.S > R.H.S
P(n) is true for n=1.

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