(n+1)(n+2)(n+3)dots(2n)

Show that the middle term in the expansion of (1+x)^(2n) is (1.32n-1)/(n!)2^(n)dot x^(n)

(n!) / ((nr)!) = n (n-1) (n-2) dots (n- (r-1))

Evaluate(with the help of definite integral): lim_(n rarr oo){(1+(1)/(n))(1+(2)/(n))dots(1+(n)/(n))}^((1)/(n))

If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)+.......+(-1)^(n-1)(2n(2n-1)(n+2))/((n-1)!)= (-1)^(n+1)(2n)!//2(n !)^2dot

If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)++(-1)^(n-1)(2n(2n-1)(n+2))/((n-1)!)=(-1)^(n+1)(2n)!//2(n !)^2dot

If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)++(-1)^(n-1)(2n(2n-1)(n+2))/((n-1)!)=(-1)^(n+1)(2n)!//2(n !)^2dot

If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)++(-1)^(n-1)(2n(2n-1)(n+2))/((n-1)!)= (-1)^(n+1)(2n)!//2(n !)^2dot

Prove that (n!)/(r!)=n(n-1)(n-2)dots(r+1)

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

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