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# Non-Inductive proof challenge.

Prove following results without induction.

1)$${ 1 }^{ 2 }+{ 2 }^{ 2 }+{ 3 }^{ 2 }+...+{ n }^{ 2 }=\frac { n\left( n+1 \right) \left( 2n+1 \right) }{ 6 }$$

2)$$1\cdot 2+2\cdot 3+3\cdot 4+....+n\left( n+1 \right) =\frac { n\left( n+1 \right) \left( n+2 \right) }{ 3 }$$

*Would like to see unique approaches.I have one. *

Note by Shivamani Patil
2 years, 10 months ago

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We could use summation in these !

- 2 years, 10 months ago

I didn't get you.Plz elaborate

- 2 years, 10 months ago