The value of `sum_(r=1)^n{(2r-1)a+1/(b^r)}` is equal to (a)`a n^2+(b^(n-1)-1)/(b^n(b-1))` . (b) `a n^2+(b^(n)-1)/(b^n(b-1))` (c) `a n^3+(b^(n-1)-1)/(b^n(b-1))` (d) none of these

The value of sum_(r=1)^(n){(2r-1)a+(1)/(b^(r))} is equal to (a)an^(2)+(b^(n-1)-1)/(b^(n)(b-1))*( b) an^(2)+(b^(n)-1)/(b^(n)(b-1)) (c) an^(3)+(b^(n-1)-1)/(b^(n)(b-1)) (d) none of these

The value of sum_(r=1)^n(-1)^(r+1)("^n C r)/(r+1) is equal to a. -1/(n+1) b. 1/n c. 1/(n+1) d. n/(n+1)

The value of sum_(r=1)^(n)(-1)^(r+1)(^nCr)/(r+1) is equal to a.-(1)/(n+1) b.(1)/(n) c.(1)/(n+1) d.(n)/(n+1)

The value of sum_(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C_(r ) is (a) 1/(n+1) (b) 1/n (c) 1/(n-1) (d) 0

The value of sum_(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C_(r ) is (a) 1/(n+1) (b) 1/n (c) 1/(n-1) (d) 0

The value of sum_(r=1)^n(sum_(p=0)^(r-1) ^nC_r ^rC_p 2^p) is equal to (a) 4^(n)-3^(n)+1 (b) 4^(n)-3^(n)-1 (c) 4^(n)-3^(n)+2 (d) 4^(n)-3^(n)

The value of sum_(r=1)^n(sum_(p=0)^(r-1) ^nC_r ^rC_p 2^p) is equal to (a) 4^(n)-3^(n)+1 (b) 4^(n)-3^(n)-1 (c) 4^(n)-3^(n)+2 (d) 4^(n)-3^(n)

The value of sum_(r=0)^n(a+r+a r)(-a)^r is equal to a. (-1)^n[(n+1)a^(n+1)-a] b. (-1)^n(n+1)a^(n+1) c. (-1)^n((n+2)a^(n+1))/2 d. (-1)^n(n a^n)/2

The value of sum_(r=0)^(n)(a+r+ar)(-a)^(r) is equal to (-1)^(n)[(n+1)a^(n+1)-a]b(-1)^(n)(n+1)a^(n+1) c.(-1)^(n)((n+2)a^(n+1))/(2)d(-1)^(n)(na^(n))/(2)

If S_n=sum_(r=1)^n(1+2+2^2+ .......+2^r)/(2^r), then S_n is equal to (a) 2^n n-1 (b) 1-1/(2^n) (c) n -1+1/(2^n) (d) 2^n-1