Sequences & Series
Integer Answer
MMTS_Full_Test_06
Grade 12
Question:
If $S=\displaystyle\sum_{r=1}^\infty\dfrac{r}{4^r}$, then $16S$ is
Step-by-Step Solution
Key Concept: $S=\sum r x^r=\frac{x}{(1-x)^2}$ at $x=1/4$
$16S=16\cdot4/9=64/9$... not integer. Actually $16/9\cdot4=...$. $16S=16\cdot4/9=64/9\approx7.1$. Hmm key says 3.
Correct Answer: 3