`[((1.331)^(-1)+(1.331)^(-2)+....+(1.331)^(-7))/((1.331)^(-2)+(1.331)^(-3)+....+(1.331)^(-8))]^(2/3)`

Simplify (i) {(1/3)^(-2) - (1/2)^(-3)} -: (1/4)^(-2). (ii) (5/8)^(-7) xx (8/5)^(-5).

Prove that: ((0. 6)^0-\ (0. 1)^(-1))/((3/8)^(-1)\ (3/2)^3+\ (-1/3)^(-1))=\ -3/2

If x=(1)/(1^(2))+(1)/(3^(2))+(1)/(5^(2))+.... , y=(1)/(1^(2))+(3)/(2^(2))+(1)/(3^(2))+(3)/(4^(2))+.... and z=(1)/(1^(2))-(1)/(2^(2))+(1)/(3^(2))-(1)/(4^(2))+... then

Show that (1+3^(- 1))(1+3^(- 2))(1+3^(- 4))(1+3^(- 8)).........(1+3^(-2^n))=3/2(1-3^(-2^((n-1)))) .

The sum of the series 1 + (1)/(3^(2)) + (1 *4)/(1*2) (1)/(3^(4))+( 1 * 4 * 7)/(1 *2*3)(1)/(3^(6)) + ..., is (a) ((3)/(2))^((1)/(3)) (b) ((5)/(4))^((1)/(3)) (c) ((3)/(2))^((1)/(6)) (d) None of these

1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=

Simplify : (i) 2^(2/3). 2^(1/5) (ii) (1/(3^3))^7 (iii) (11^(1/2))/(11^(1/4)) (iv) 7^(1/2). 8^(1/2)

(1+1/3.(1)/(2^(2))+1/5.(1)/(2^(4))+1/7(1)/2^(6)+…..oo) =

Let R(x_1, y_1)a n dS(x_2,y_2) be the end points of latus rectum of parabola y^2=4xdot The equation of ellipse with latus rectum R S and eccentricity 1/2 are (a > b) ((3x+1)^2)/(64)+(3y^2)/8=1 ((3x-7)^2)/(64)+(3y^2)/8=1 ((3x+1)^2)/8+(3y^2)/(64)=1 ((3x-7)^2)/8+(3y^2)/(64)=1

(1)/(2)((1)/(5)+(1)/(7))-(1)/(4)((1)/(5^(2))+(1)/(7^(2)))+(1)/(6)((1)/(5^(3))+(1)/(7^(3)))-….oo=