<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find $\sum\limits_{r=N+1}^{2N}{\left( {{2}^{r}}+{{3}^{N}} \right)}$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">The ${{n}^{\mathrm{th}}}$ term, ${{u}_{n}}$, of a series is given by ${{u}_{n}}=\frac{1}{{{n}^{2}}+n}-\frac{1}{{{n}^{2}}+3n+2}$.</span></div><div class="list-item-paragraph">Find $\sum\limits_{n=1}^{N}{{{u}_{n}}}$ in terms of $N$.</div><div class="list-item-paragraph">Explain why $\sum\limits_{n=1}^{\infty }{{{u}_{n}}}$ is a convergent series, and state the value of the sum to infinity.</div><p style="text-align: right;">[5]</p></li></ol>

Find $\sum\limits_{r=N+1}^{2N}{\left( {{2}^{r}}+{{3}^{N}} \right)}$.

The ${{n}^{\mathrm{th}}}$ term, ${{u}_{n}}$, of a series is given by ${{u}_{n}}=\frac{1}{{{n}^{2}}+n}-\frac{1}{{{n}^{2}}+3n+2}$.

Find $\sum\limits_{n=1}^{N}{{{u}_{n}}}$ in terms of $N$.

Explain why $\sum\limits_{n=1}^{\infty }{{{u}_{n}}}$ is a convergent series, and state the value of the sum to infinity.

2018 RI Promo Q6

2018 RI Promo Q6

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