Evaluate: `sum_(r=1)^n(3^r-2^r)`

sum_(r=1)^(n)(3^(r)-r)=

Evaluate: sum_(r=1)^n (1^3 + 2^3 + 3^3 + …. + r^3) / (r+1)^2

Evaluate : sum_(r=1)^n (r+1)(r+3)

Evaluate sum_(r=0)^n(r+1)^2*"^nC_r

Evaluate : sum_(r = 1)^(n) ""^(n)C_(r) 2^r

Evaluate sum_(r = 1)^(n) ""^nC_r 2^r

Find sum_(r=1)^n (2/3)^r

Find the sum sum_(r=1)^n (3r^2 - 2r + 1)

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .