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

If z=(1)/(3)+(1.3)/(3.6)+(1.3.5)/(3.6.9)+.... then

Which term of the GP sqrt(3), 1/sqrt(3), 1/(3sqrt(3)), 1/(9sqrt(3)) , ... Is 1/(729sqrt(3)) ?

5(1)/(6)-3(1)/(4)+3(1)/(3)+4

(6) (1)/(3)-:(3)/(10) of (11)/(9)+(5)/(6)

(1+(1)/(3)+(1)/(3)*(3)/(3)+(1)/(3)*(5)/(9)*(5)/(9)+(1)/(3)*(3)/(6)*(5)/(9)*(7)/(12)+)^(2)

Q.the sum of the infinite series 1+(2)/(3)*(1)/(2)+(2)/(3)*(5)/(6)*(1)/(2^(2))+(5)/(3)*(5)/(6)*(8)/(9)*(1)/(2^(3))+... is

The sum of the infite series (1/3)^(2)+1/3(1/3)^(4)+1/5(1/3)^(6) +……..is

If y = (1)/(3) + (1*3)/(3 *6) + (1 * 3*5)/(3*6*9) +… then the value of y^(2) + 2y is

5(5)/(6) -3(8)/(9) -? =1