2014 RVHS Promo Q2
The sum of the first $n$ terms of a progression is given by ${{S}_{n}}=1-{{\text{e}}^{2n}}$.
(i)
Find ${{U}_{n}}$, the $n$th term of the progression.
[2]
(ii)
Prove that ${{U}_{1}}$, ${{U}_{2}}$, ${{U}_{3}}$… is a geometric progression. Hence determine if the sum ${{S}_{n}}$ converges.
[3]
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