2011/022) To show that 1 = 1/2+1/4+ 1/8 + 1/16+ ….

We can prove from the RHS that

1/2+1/4+ 1/8 + 1/16+ .. is a GP with a= 1/2 and r = 1/2 and the GP converges to

1/2/(1-/12) = 1/2/(1/2) = 1

but beauty lies in expanding from LHS

1 = 1/2 + 1/2
= 1/2 + 1/4 + 1/4 ( take the last term and make into 2 halves)
= 1/2 + 1/4 + 1/8 + 1/8 and so on to get the result