If ` x = (1.3)/(3.6) + (1.3.5)/(3.6.9) + (1.3.5.7)/(3.6.9.12) + …..` then prove that `9x^2 + 24x = 11`

Show that 1 + 1/3 + (1.3)/(3.6) + (1.3.5)/(3.6.9) + ….. = sqrt3

If x = (1*3)/(3*6)+(1*3*5)/(3*6*9)+(1*3*5*7)/(3*6*9*12)+. . . to infinite terms, then 9x^(2) + 24 x =

Sho that 3/6 + (3.5)/(6.9) + (3.5.7)/(6.9.12)+ ……..oo 3 sqrt3 - 4

If 3x + (1)/(3x) = 3 , find : (i) 9x^(2) + (1)/(9x^2)

If 3x - (1)/(3x ) =5 , find : (i) 9x^(2) + (1)/( 9x^2)

Which is greater: (5)/(6) of (3)/(4) or (3)/(12) of (11)/(9) ?

For x in(0,1) arrange f_(1)(x) = (1)/(9-x^(2)), f_(2)(x) = (1)/(9-2x^(2)) and f_(3)(x) = (1)/(9-x^(2)-x^(3)) in ascending order and hence prove that 1/6 ln2 lt int_(0)^(1)(1)/(9-x^(2)-x^(3)) dx lt (1)/(6sqrt(2)) ln 5 .

The sum of the series 5/(1. 2.3)+7/(3. 4.5)+9/(5. 6.7)+ ....is equal to

Show that sqrt3 =1+ 1/3 +( 1/3 ).( 3/6 )+(1/3)*((3/6)*(5/9)*(7/12)+.......

If y=(2x^9)/3-5/7x^7+6x^3-x , find (dy)/(dx) at \ x=1 .