" The sum of the infinite series "1+(1+(1)/(2))((1)/(3))+(1+(1)/(2)+(1)/(2^(2)))((1)/(3^(2)))+.......00" is "

The sum of the infinite series 1+(1+(1)/(2))((1)/(3))+(1+(1)/(2)+(1)/(2^(2)))((1)/(3^(2)))+...oo

The sum of the infinite series 1+(1+(1)/(5))((1)/(2))+(1+(1)/(5)+(1)/(5^(2)))((1)/(2^(2)))+

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

The sum of the infinite series (1)/(2) ((1)/(3) + (1)/(4)) - (1)/(4)((1)/(3^(2)) + (1)/(4^(2))) + (1)/(6) ((1)/(3^(3)) + (1)/(4^(3))) - ...is equal to

The sum of the infinite series 1+(1+1/5)(1/2)+(1+1/5+1/(5^2))(1/(2^2))+...

The sum of the infinite series 1+(1+1/5)(1/2)+(1+1/5+1/(5^2))(1/(2^2))+...

The sum to the infinite series,1+2(1-(1)/(n))+3(1-(1)/(n))^(2)+...... is

Prove that : Find the sum of the infinite series 1+(2)/(3).(1)/(2)+(2.5)/(3.6)((1)/(2))^(2)+(2.5.8)/(3.6.9)((1)/(2))^(3)+......oo