if `x<1` then `1/(1+x)+(2x)/(1+x^2)+(4x^3)/(1+x^4)+..............oo`

If f(x)=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)):}| then

Using the properties of determinants, solve the following for x |{:(a+x,a-x,a-x),(a-x,a+x,a-x),(a-x,a-x,a+x):}|=0

Using properties of determinants, solve for x:|[a+x, a-x, a-x],[ a-x, a+x, a-x],[ a-x, a-x, a+x]|=0

Using properties of determinants, solve for x:|[a+x, a-x, a-x], [a-x, a+x, a-x], [a-x, a-x ,a+x]|=0

Using properties of determinants, solve for x:|[a+x, a-x, a-x],[ a-x, a+x, a-x],[ a-x, a-x, a+x]|=0

Using properties of determinants solve the following for x, |{:(x+a,x,x),(x,x+a,x),(x,x,x+a):}|=0

Using Properties of determinants, solve the following for x: {:|(x+a,x,x),(x,x+a,x),(x,x,x+a)|=0

If f(x) = |(x + lamda,x,x),(x,x + lamda,x),(x,x,x + lamda)|, " then " f(3x) - f(x) =

If f(x)=|[x+lambda,x,x] , [x,x+lambda,x] , [x,x,x+lambda]| then f(12x)-f(x)=