26.2x^(2)-(5)/(6)x+(1)/(12)

Show that the sum of the coefficients of x^(-6) and x^(-1) in (5x^(2)-(7)/(x^(3)))^(12) is positive.

If (1+x-2x^(2))^(6)=1+a_(1)x+a_(2)x^(12)+...+a_(12)x^(12) then find the value of a_(2)+a_(4)+a_(6)+...+a_(12)

If (1+x-2x^(2))^(6)=1+a_(1)x+a_(2)x^(2)+….+a_(12)^(x^(12)) , then find the value of a_(2)+a_(4)+a_(6)+….+a_(12) .

(1+x-2x^(2))^(6)=1+a_(1),x+a_(2)x^(2)+….+a_(12)^(12) then the value of a_(2) +a_(4)+a_(6)+….+a_(12)=………

(x+1)/(2)+(x-1)/(3)=(5)/(12)(x-2)

If f(x)=int_(1)^(x^(3))(dt)/(1+t^(4)), then f'(x) is equal (6x((1-5x^(2))^(12)))/((1+x^(12))^(12))) (ii) (6x((1+5x^(2))^(12)))/((1+x^(12))^(2))( (iii) -(6x((1-5x^(2))^(12)))/((1+x^(12))^(2)) (iv) none of these

The series expansion of log[(1 + x)^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]