The sum of the first $n$ terms of a progression is given by ${{S}_{n}}=1-{{\mathrm{e}}^{2n}}$. F

Question

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

Accepted Answer

(i) ${\mathrm{e}^{2(n-1)}(1-\mathrm{e}^2)}$ or ${\mathrm{e}^{2n}\left(\mathrm{e}^{-2}-1\right)}$ (ii) ${S_n}$ does not converge.

2014 RVHS Promo Q2

2014 RVHS Promo Q2

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