$$\frac{7}{8} – \frac{49}{64} + \frac{343}{512}…$$
I make the guess that this is suppose to be represented as
$$-1^{n+1} * (\frac{7}{8})^n$$
Now I use the formula my book gives
$$\Sigma_{n=M}^\inf -1^{n+1} = \frac{cr^M}{1 – r}$$
$$ \Sigma_{n=1}^\inf -1^{n+1} * (\frac{7}{8})^n$$
$$\frac{-1 \frac{7}{8}}{1 – \frac{7}{8}}$$
Why is this wrong? I copied the formula exactly and my representation of the series is correct.
Best Answer
Define
$$a=\frac78\;,\;\;q=-\frac78$$
Thus
$$|q|<1\implies \sum_{n=0}^\infty aq^n=\frac a{1-q}=\frac{\frac78}{1+\frac78}=\frac7{15}$$