Q. if `x_1,x_2......x_n` are in `H.P`., then `sum_(r=1)^n x_r x_(r+1)` is equal to `:` (A) `(n-1)x_1 x_n` (B) `n x_1 x_n` (C) `(n+1)x_1 x_n` (D) `(n+2)x_1 x_n`

If x_(1),x_(2),x_(3),......x2_(n) are in A.P, then sum_(r=1)^(2n)(-1)^(r+1)x_(r)^(2) is equal to

If x_1, x_2, x_3,...... x _(2n) are in A.P , then sum _(r=1)^(2n) (-1)^(r+1) x_r^2 is equal to (a) (n)/((2n-1))(x _(1)^(2) -x _(2n) ^(2)) (b) (2n)/((2n-1))(x _(1)^(2) -x _(2n) ^(2)) (c) (n)/((n-1))(x _(1)^(2) -x _(2n) ^(2)) (d) (n)/((2n+1))(x _(1)^(2) -x _(2n) ^(2))

If X = [{:( 1,1), ( 1,1):}]then X ^(n) , for n in N, is equal to : a) 2 ^(n -1) X b) n ^(2)X c) nX d) 2 ^(n +1) X

If 1+x^(2)=sqrt(3)x, then sum_(n=1)^(24)(x^(n)-(1)/(x^(n))) is equal to

(1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + ...+ C_(n) x^(n) , show that sum_(r=0)^(n) C_(r)^(3) is equal to the coefficient of x^(n) y^(n) in the expansion of {(1+ x)(1 + y) (x + y)}^(n) .

(1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + ...+ C_(n) x^(n) , show that sum_(r=0)^(n) C_(r)^(3) is equal to the coefficient of x^(n) y^(n) in the expansion of {(1+ x)(1 + y) (x + y)}^(n) .

If sum_(r=1)^(n)Cos^(-1)x_(r)=0," then "sum_(r=1)^(n)x_(r) equals to

If sum_(r=1)^(n)cos^(-1)x_(r)=0, then sum_(r=1)^(n)x_(r) equals to

By method of induction, prove that sum_(r=1)^n ax^(r-1) = a ((1-x^n)/(1-x)) , for all n in N , x != 1 .