inequality `(1+x)^n> 1 + nx`, (wherever x is positive and n is a positive integer).

Prove by induction the inequality (1+x)^ngeq 1+n x whenever x is positive and n is a positive integer.

Solve (x - 1)^n =x^n , where n is a positive integer.

Prove that (""^n C_0)/x-(""^n C_1)/(x+1)+(""^n C_2)/(x+2)-.....+(-1)^n(""^n C_n)/(x+n)=(n !)/(x(x+1) . . . (x-n)), where n is any positive integer and x is not a negative integer.

If f(x)=(a-x^(n))^(1//n) , where a gt 0 and n is a positive integer, then f[f(x)]=

int (dx)/(1+nsqrt(x+1)) , n is a positive integer.

If ((1+i)/(1-i))^x=1 then (A) x=2n+1 , where n is any positive ineger (B) x=4n , where n is any positive integer (C) x=2n where n is any positive integer (D) x=4n+1 where n is any positive integer

(x+1) is a factor of x^(n)+1 only if n is an odd integer (b) n is an even integer n is a negative integer (d) n is a positive integer

Prove that (^n C_0)/x-(^n C_0)/(x+1)+(^n C_1)/(x+2)-+(-1)^n(^n C_n)/(x+n)=(n !)/(x(x+1)(x-n)), where n is any positive integer and x is not a negative integer.

Solve (x-1)^(n)=x^(n), where n is a positive integer.