Tuesday, November 12, 2013

Q13/116) 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

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