Prove that : `(r_1)/((s-b)(s-c))+(r_2)/((s-c)(s-a))+(r_3)/((s-a)(s-b))=3/r`

Prove that : (r_1)/(b c)+(r_2)/(c a)+(r_3)/(a b)=1/r-1/(2R)

If S=a+b+c then prove that (S)/(S-a)+(S)/(S-b)+(S)/(S-c) gt (9)/(2) where a,b & c are distinct positive reals.

If in Delta ABC, (a -b) (s-c) = (b -c) (s-a) , prove that r_(1), r_(2), r_(3) are in A.P.

Let S_n denote the sum of first n terms of a G.P. whose first term and common ratio are a and r respectively. On the basis of above information answer the following question: S_1+S_2+S_3+..+S_n= (A) (na)/(1-r)-(ar(1-r^n))/((1-r)^2 (B) (na)/(1-r)-(ar(1+r^n))/((1+r)^2 (C) (na)/(1-r)-(a(1-r^n))/((1-r)^2 (D) none of these

Prove that underset(rles)(underset(r=0)overset(s)(sum)underset(s=1)overset(n)(sum))""^(n)C_(s) ""^(s)C_(r)=3^(n)-1 .

Prove that sum_(r=0)^ssum_(s=1)^n^n C_s^n C_r=3^n-1.

Prove that ("a c o s"A+b cosB+c cosC)/(a+b+c)=r/Rdot

If c^(2) = a^(2) + b^(2) , then prove that 4s (s - a) (s - b) (s - c) = a^(2) b^(2)

Prove that ("a c o s"A+b cosB+ccosC)/(a+b+c)=r/Rdot

If S_(n) = underset (r=0) overset( n) sum (1) /(""^(n) C_(r)) and T_(n) = underset(r=0) overset(n) sum (r )/(""^(n) C_(r)) then (t_(n))/(s_(n)) = ?