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1^(2)+1+2^(2)+2+3^(2)+3+......+n^(2)+n=...

1^(2)+1+2^(2)+2+3^(2)+3+......+n^(2)+n=

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P(n) : 1^(2) + 2^(2) + 3^(2) + .......+ n^(2) = n/6(n+1) (2n+1) n in N is true then 1^(2) +2^(2) +3^(2) + ........ + 10^(2) = .......

1 ^(2) + 2^(2) + 3^(2) + . . . + n^(2) = (n (n + 1) (2 n + 1))/( 6)

Match the following . {:(,"ColumnI",,"ColumnII"),((i) ,1^(2) +2^(2) +3^(2) +....+n^(2) ,(a) ,[(n(n+1))/(2)]^(2)),((ii) , 1^(3) +2^(3) +3^(3) +...+n^(3) ,(b), n(n+1)),((iii),2+4+6+...+2n,( c),(n(n+1)(2n+1))/(6)),((iv),1+2+3+...+n,(d),(n(n+1))/(2)):}

Match the following . {:(,"ColumnI",,"ColumnII"),((i) ,1^(2) +2^(2) +3^(2) +....+n^(2) ,(a) ,[(n(n+1))/(2)]^(2)),((ii) , 1^(3) +2^(2) +3^(2) +...+n^(3) ,(b), n(n+1)),((iii),2+4+6+...+2n,( c),(n(n+1)(2n+1))/(6)),((iv),1+2+3+...+n,(d),(n(n+1))/(2)):}

1^(2)+2^(2)+3^(2)+..........+n^(2)=(n(n+1)(2n+1))/(6)

Prove that 1^(2)+2^(2)+3^(2)+.....+n^(2)=(n(n+1)(2n+1))/6

Prove by mathematical induction 1^(2)+2^(2)+3^(2)+.....+(n+1)^(2)=((n+1)(n+2)(n+3))/(6)

lim_ (n rarr oo n rarr oo) (1.n ^ (2) +2 (n-1) ^ (2) +3 (n-2) + ... + n.1 ^ (2)) / ( 1 ^ (3) + 2 ^ (3) + ... n ^ (3))