`sum_(r=1)^ntan(x/(2^r))sec(x/(2^(r-1))); r , n in N`

lim_(n->oo) sum_(r=1)^ntan^(- 1)((2r+1)/(r^4+2r^3+r^2+1)) is equal to

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of sum_(r=0)^(n)a_(r) is

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of sum_(r=0)^(n)a_(r) is

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

sum_(r=1)^ntan^-1((x_r-x_(r-1))/(1+x_(r-1)x_r))=sum_(r=1)^n(tan^-1x_r-tan^-1x_(r-1))=tan^-1x_n-tan^-1x_0, AAn in N Answer the following question on above passage: The sum to infinite terms of the series cot^-1(2^2+1/2)+cot^-1(2^3+1/2^2)+cot^-1(2^4+1/2^3)+ ..... is

The value of lim_( n to oo) sum_(r =1)^(n) (r )/(n^(2))"sec"^(2)(r^(2))/(n^(2)) is equal to -

If (1-x^(2))^(n)=sum_(r=0)^(n)a_(r)x^(r)(1-x)^(2n-r), then a_(r) is equal to ^(n)C_(r) b.^(n)C_(r)3^(r) c.^(2n)C_(r) d.^(n)C_(r)2^(r)

lim_(n rarr oo) sum_(r=1)^(n) r/n^(2) sec^(2) (r^(2)/n^(2)) =

lim_(x rarr2)(sum_(r=1)^(n)x^(r)-sum_(r=1)^(n)2^(r))/(x-2)