" (ii) "1^(2)+2^(2)+3^(2)+.........+n^(2)<=(n)/(3)

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) = .......

Find the mean,variance and standard deviation of the series 1^(2),2^(2),3^(2),.........,n^(2)

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

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

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

By Principle of Mathematical Induction, prove that : 1+2+3+.....+n=n(n+1)/(2) 1^(2)+2^(2)+3^(2)+......+n^(2)=(1)/(6)n(n+1)(2n+1) for each given n in N

What is lim_(ntooo) (1+2+3+......+n)/(1^(2)+2^(2)+3^(2)+......n^(2))

Evaluate the following limits : Lt_(ntooo)(1^(2)+2^(2)+3^(2)+......+n^(2))/n^(3)

Evaluate Lt_(ntooo)(1^(2)+2^(2)+3^(2)+......+n^(2))/n^(3) .

The number of positive integers n in the set {1, 2, 3, .......100} for which the number (1^(2)+2^(2)+3^(2)+......+n^(2))/(1+2+3+......+n) is an integer is