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

Evaluate the following: sum_(n=1)^(11)(2+3^(n))

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 of the following series : (1)/(4) + (1)/(2) + 1 + … to n terms

Evaluate sum_(n=1)^n (n^2+n-1)/((n+2)!) .

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 :

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 :

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