The sum, ${{S}_{n}}$, of the first $n$ terms of a sequence ${{u}_{1}}$, ${{u}_{2}}$, ${{u}_{3}}$ ...

Question

The sum, ${{S}_{n}}$, of the first $n$ terms of a sequence ${{u}_{1}}$, ${{u}_{2}}$, ${{u}_{3}}$ ... is given by ${{S}_{n}}=\ln \left( n+1 \right)$ Find ${{u}_{n}}$ in terms of $n$. [2] Describe the behaviour of the sequence. [1]

Accepted Answer

(i) $u_n=\ln\left(\frac{n+1}{n}\right)$ (ii) Decreasing and convergent to $0$

2020 TJC Promo Q1

2020 TJC Promo Q1

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