You need to remember how to evaluate the sum of n terms of geometric progression such that:
`S_n_1 = (a_1)*(r^n - 1)/(r-1)`
Notice that 1 represents the value of the first terms of geometric progression and r represents the common ratio.
You need to evaluate the sum of the n terms of the same geometric progression, having the first term `n+1` and the same common ratio r such that:
`S_n_2 = (a_(n+1))*(r^n - 1)/(r-1)`
You need to evaluate the following ratio such that:
`(S_n_1)/(S_n_2) = ((a_1)*(r^n - 1)/(r-1))/(a_(n+1)*(r^n - 1)/(r-1))`
Reducing like terms yields:
`(S_n_1)/(S_n_2) = (a_1)/(a_(n+1))`
You need to remember that you may write the `a_(n+1)` term using the first term and the common ratio such that:
`(a_(n+1)) = a_1*r^n`
`(S_n_1)/(S_n_2) = (a_1)/(a_1*r^n)`
Reducing like terms yields:
`(S_n_1)/(S_n_2) = 1/r^n`
Hence, evaluating the ratio `(S_n_1)/(S_n_2)` yields `(S_n_1)/(S_n_2) = 1/r^n` .
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