`1 + 1/2 + 1/(2^2)+………., r = ……………….`

In a triangleABC , if 1/r^(2) + 1/r_(1)^(2) + 1/r_(2)^(2) + 1/r_(3)^(2) = (a^(2) + b^(2) + c^(2))/(Delta^(n)) , then n is equal to ………..

In a triangleABC , if 1/r^(2) + 1/r_(1)^(2) + 1/r_(2)^(2) + 1/r_(3)^(2) = (a^(2) + b^(2) + c^(2))/(Delta^(n)) , then n is equal to ………..

Find sum_(r=1)^n (1^2 + 2^2 + 3^2 + ………. + r^2) / (2r +1)

Find sum_(r=1)^n (1^2 + 2^2 + 3^2 +…….+ r^2) / (r + 1)

In Delta ABC , ( Delta ^(2))/( a^(2) + b^(2) + C^(2)) {(1)/( r_1^(2) ) + ( 1)/( r_2^(2) ) +(1)/( r_3^(2)) +(1)/( r^(2)) } =

If P_(r) is the coefficient of x^® in the expansion of (1 + x)^(2) (1 + (x)/(2))^(2) (1 + (x)/(2^(2)))^(2) (1 + (x)/(2^(3)))^(2)... prove that P_(r) = (2^(2))/((2^(r) -1))(P_(r-1) + P_(r-2) )and P_(4) = (1072)/(315) .

If a = sum_(r=1)^(oo) 1/(r^(2)), b = sum_(r=1)^(oo) 1/((2r-1)^(2)), then (3a)/b is equal to _____