Example $2$. A sequence $\{u_n\}$ is defined by $u_n = \frac{(-1)^n}{n}, n = 1, 2, 3, \dots$ W

Question

Example $2$. A sequence $\{u_n\}$ is defined by $u_n = \frac{(-1)^n}{n}, n = 1, 2, 3, \dots$ Write down the first four terms of this sequence. Explain why $-\frac{1}{144}$ is not a term of $\{u_n\}$. (Hint: Use a proof by contradiction.) Another sequence $\{v_n\}$ is formed by taking the $1^{\mathrm{st}}$, $3^{\mathrm{rd}}$, $5^{\mathrm{th}}$, and in general, all the odd-positioned terms of $\{u_n\}$. Write, in terms of $n$, an expression for $\{v_n\}$.

Accepted Answer

(i) $-1,\dfrac12,-\dfrac13,\dfrac14$ (ii) $k=144$ would give a positive term, a contradiction. (iii) $v_n=-\dfrac1{2n-1}$, $n\ge1$

Terms of a sequence

Terms of a sequence

Solution:

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