Find the following sum: `1/(n !)+1/(2!(n-2)!)+1/(4!(n-4)!)+. . . .`

Find the sum of the following. (1-(1)/(n))+(1-(2)/(n))+(1-(3)/(n))+... up to n terms.

Prove that (1)/(n!)+(1)/(2!(n-2)!)+(1)/(4!(n-4)!)+...=(1)/(n!)2^(n-1)

Find the sum to n terms of each of the following series : n.1 + (n-1).2+(n-2). 3+(n-3).4+…

Find the sum of the following: 1.2+2.3+…..+n(n+1)

Find the sum: sum_(n=1)^(10){(1/2)^(n-1)+(1/5)^(n+1)}dot

Find the sum sum_(j=0)^(n) (""^(4n+1)C_(j)+""^(4n+1)C_(2n-j)) .

Find sum the series (n)/(1.2*3)+(n-1)/(2.3*4)+(n-2)/(3.4*5)+......... up to n terms..-

Let S_n = 1 (n - 1) + 2. (n -2) + 3. (n - 3) +…+ (n -1).1, n ge 4. The sum sum_(n = 4)^oo ((2S_n)/(n!) - 1/((n - 2)!)) is equal to :