[" BHRAG "7" sialls adl at "],[qquad 1^(2)+2^(2)+......+n^(2)>(n^(3))/(3),n in N]

1^(3)+2^(3)+3^(3)+.....+n^(3)=(n(n+1)^(2))/(4), n in N

Prove by PMI that 1.2+2.3+3.4+....+n(n+1)=((n)(n+1)(n+2))/(3),AA n in N

1.3+2.4+3.5+....+n(n+2)=(n(n+1)(2n+7))/(6)

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) = .......

lim_(n to oo) [ 1^2/n^3 + (2^2)/(n^3) + …+ ((n-1)^2)/(n^3)]

Prove that 1*2+2*3+3*4+.....+n*(n+1)=(n(n+1)(n+2))/(3)

1.2+2.3+3.4+.........+n(n+1)=(1)/(3)n(n+1)(n+3)

AA n in , 7^(2n) + 3^(n-1) . 2^(3n-3) is divisible by

1.2.3+2.3.4+....+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4

If n is a natural number then show that 1.3.5.7…..(2n-1) = ((2n)!)/(2^n n!)