Bob cranked up his sound system. Initially, the volume is set to v>0.

At the end of each second, the control circuitry performs two adjustments:

1.) it resets the volume to the square root of its value

then,

2.) it increases the reset volume by the intial volume, v.

Performing these two operations always increases the volume:

initial volume: v(0) = v

volume after first adjustment:

v(1) = v(0) + sqr(v(0)) = v + sqr(v)

volume after second adjustment:

v(2) = v(1) + sqr(v(1))

= v(0) + sqr(v(0) + sqr(v(0))

= v + sqr(v + sqr(v))

volume after third adjustment:

v(3) = v + sqr(v + sqr(v + sqr(v)))

etc., and obviously v = v(0) < v(1) < v(2) < v(3) < ...

If this process continues indefinately, will the volume converge to a finite value? if so, what value?