Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that `P^2R^n=S^ndot`

Explanation

Let G.P. be
`a,ar,ar^2,....ar^(n−1)`

`S=(a(r^n−1))/(r-1)​`
`P=a^nr^(((n−1)n)/2​)`


`R=1/a​+1/(a^r)​+1/(ar^2)`

​`=(1​(r^0+r^(−1)+r^(−2)+....))/a`

`=1/a​×r^0(r^n−1)/(r^n−1​)`

`=1/a​(1−r^n×r​)/(r^n(1−r))`

`=((1−r^n)(r^(1−n))​)/(a(1−r))`

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