I'm getting a bit puzzled with regards to this question:

I'm not really sure where to start with this except to state that 0.4 is an upper bound of the sequence. That isn't really enough for the start bit and I can't see what the next step would be.Explain why is never larger than 0.4 given that:

.

Hence show that the error in calculating reduces by at least 0.4 when replacing n by 2n. Show that by calculating and we can estimate to within 0.0014.

Okay, this may help a lot but i've just worked out that where tends to from above. Therefore the first bit should go a little something like this:

The big problem here is that it doesn't give the required 0.4.

I'm also not sure if thiis helps but and .