The value of `3(1)/(2)-[2(1)/(4)-{1(1)/(4)-(1)/(2)(1(1)/(2)-(1)/(3)-(1)/(6))}]`

3log 2 +(1)/(4) -(1)/(2)((1)/(4))^(2)+(1)/(3)((1)/(4))^(3)-….. =

(1)/(1.2)+(1)/(3.4)+(1)/(5.6)+....

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...

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!)+(1)/(2!)+(1)/(4!)+(1)/(6!)+…)-(1/(1/(1)+(1)/(3!)+(1)/(5!)+…)) is equal to

The value of log_((9)/(4))((1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3)))))...oo) is

The value of (1)/((1+a)(2+a))+(1)/((2+a)(3+a))+(1)/((3+a)(4+a))"......." " upto " oo is (where, a is constant)

If ((3(1)/(4) )^(4) -(4( 1)/(3))^(4))/( (3,(1)/(4) )^(2) -(4,(1)/(3))^(2) )= ((13a)/(12))^(2) , find a.

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

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