Find the value of `((n),(m))+((n-1),(m))+((n-2),(m))+...+((m),(m))`.

(b) Find the value of sum_(r=m)^(n)*Cm,n>m

The value of (m+n)^2+(m-n)^2 is

Find the value of ( m^4 - m^2n^2) ÷ m^2 is

Find the squre root of (m^(n^(2)) n^(m^(2)) a^((m +n)))/((m + n)^((m +n)^(2)))

^(n)C_(m)+^(n-1)C_(m)+^(n-2)C_(m)+............+^(m)C_(m)

Find the square root of (m^(n^(2))n^(m^(2))a^((m+n)))/((m+n)^((m+n)^(2) (i) (m^n)(n^m)a^((m+n)/2) (ii) ((m^(n^2))(n^(m^2))a^((m+n)/2))/(m+n)^(((m+n)^2)/2) (iii) (m^n)(n^m)a^(sqrt(m+n))/(m+n)^(((m+n))) (iv)none of these

Find the value of sum_(p=1)^(n)(sum_(m=p)^(n)C_(m)^(m)C_(p)) And hence,find the value of lim_(n rarr oo)(1)/(3^(n))sum_(p=1)^(n)(sum_(m=p)^(n)C_(m)^(m)C_(p))

What is the value of tan^(-1)((m)/(n))-tan^(-1)((m-n)/(m+n)) ?