Thread: Sum G.P. question

If "S" be the sum, P the product, and R the sum of the reciprocals of "n" terms in G.P, prove that ;


can anyone help me out? Thanks

Rather than help out with this obvious homework question, I am only going to give you a hint.

(quite obviously)

while


i.e.

If you're not quite sure how I got that, think back to the laws of exponents and the good old sum of an arithmetic progression.

Now for R.



Believe it or not, this is actually a geometric progression too, only with a different first term and a different common ratio. It's quite easy to figure out the sum of this GP, if you think of it.

Then simply solve separately for the right and left hand sides of the equation, and show that they are equal.