square root infinite series | 2sec

The sum of an infinite geometric series is 2 and the sum of the geometric series made from the cubes of this infinite series is 24. Then the series is:

Find the resistance of the infinite series of the circuit in figure between the points a and b. [Hint: From an infinite series if we separate out the first unit, the remaining circuit will still be an infinite series and hence will have the same equivalent resistance]

If A is a square matrix of order 2xx2 such that |A|=27 , then sum of the infinite series |A|+|1/2A|+|1/4 A|+|1/8 A|+... is equal to _______ .

The sum of the infinite series (2^(2))/(2!) + (2^(4))/(4!) + (2^(6))/(6!) + ... Is equal to