[" Kxample "6." Prove that "],[2.6.10.14..." to "n" factors "=((2n)!)/(n!)=(n+1)(n+2)..." to "n" factors."]

Show that 2.6.10……. to n factors =((2n)!)/(n!)

Show that 2.6.10.14.. To n factors =(n+1)(n+2)(n+3) … to n factors.

the continued product 2.6.10.14... to n factors is equal to 2np_(n)(b)^(2n)C_(n)(n+1)(n+2)(n+3)...(n+n)2^(n)*(1.3.5......2n-1)

Factor n^(2)-5n-14 .

Prove that 2 + 4 + 6 + .... + 2n = n (n + 1)

By method of induction, prove that 1.6 + 2.9 + 3.12 +... +to n terms = n(n +1 )(n+2) for all n in N .

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

Prove that 2.4.6.8..........2n<(n+1)^(n)*(n in N)

Given that P(n, r)=n(n-1)(n-2) ….to r factors If P(n, 4) = 20 P(n, 2), find n

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