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Question

12+2232+42+5262+72+8292+.... to 3n terms.

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Solution

12+2232+42+5262+....... to 3n terms
=(12+22+32+42+52+........+(3n)2)
2(32+62+......+(3n)2)
=(11+22+........+(3n)2)2.9(12+22+........+n2)
=3n.(3n+1)(6n+1)618n(n+1)(2n+1)6
=n(3n+1)(6n+1)23n(n+1)(2n+1)
=n[6n29n52]

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