Sequences & Series
Sum of Series
MMTS_Full_Test_15
Grade 12
Question:
$1+\dfrac{2}{3}+\dfrac{2\cdot5}{3\cdot6}+\dfrac{2\cdot5\cdot8}{3\cdot6\cdot9}+\cdots$
$3^{1/3}$
$2^{2/3}$
$3^{2/3}$
$2^{1/3}$
Step-by-Step Solution
Key Concept: This series is related to binomial expansion $(1-x)^{-n}$
Series matches $(1-1/3)^{-2/3}=(2/3)^{-2/3}=3^{2/3}/2^{2/3}$... Alternatively: $=3^{1/3}$.
Correct Answer: 3