" (1) "r=0+sqrt(3)" find "x^(2)+(1)/(n)

Evaluate lim _( n to oo) sum_( r =1) ^(n -1) (1)/(sqrt(n ^(2) -r ^(2)))

Statement -2: sum_(r=0)^(n) (-1)^( r) (""^(n)C_(r))/(r+1) = (1)/(n+1) Statement-2: sum_(r=0)^(n) (-1)^(r) (""^(n)C_(r))/(r+1) x^(r) = (1)/((n+1)x) { 1 - (1 - x)^(n+1)}

Statement -2: sum_(r=0)^(n) (-1)^( r) (""^(n)C_(r))/(r+1) = (1)/(n+1) Statement-2: sum_(r=0)^(n) (-1)^(r) (""^(n)C_(r))/(r+1) x^(r) = (1)/((n+1)x) { 1 - (1 - x)^(n+1)}

Statement-1: sum_(r =0)^(n) (r +1)""^(n)C_(r) = (n +2) 2^(n-1) Statement -2: sum_(r =0)^(n) (r+1) ""^(n)C_(r) x^(r) = (1 + x)^(n) + nx (1 + x)^(n-1)

Statement-1: sum_(r =0)^(n) (r +1)""^(n)C_(r) = (n +2) 2^(n-1) Statement -2: sum_(r =0)^(n) (r+1) ""^(n)C_(r) x^(r) = (1 + x)^(n) + nx (1 + x)^(n-1)

Evaluate : lim_( x -> 0 )( sqrt( 3 -x ) -1 )/ ( 2-x )

Let the variable x_(n), be determined by the following law of formation 0x_(0)=sqrt(a)x_(0)=sqrt(a),x_(1)=sqrt(a+sqrt(a))x_(2)=sqrt(a+sqrt(a+sqrt(a))) and x_(3)=sqrt(a+sqrt(a+sqrt(a+sqrt(a)))) then find lim_(n rarr1)x_(n)

Find the simplest value of f(x)=tan^(-1)((sqrt(1+x^(2))-1)/(x)),x in R-{0}