Sequences & Series
Sum of Series
MMTS_Full_Test_06
Grade 12
Question:
If $S_n=0.7+0.77+0.777+\cdots$ to $n$ terms, then $S_n=$
$\dfrac{7}{81}(9n-1+10^{-n})$
$\dfrac{7}{81}(9n-1+10^{-n})$
$\dfrac{7}{9}(n-\frac{1-10^{-n}}{9})$
$\dfrac{7}{81}(9n+1-10^{-n})$
Step-by-Step Solution
Key Concept: $0.777...7$ ($r$ digits) $= 7/9(1-10^{-r})$
$S_n=\frac{7}{9}(n-\frac{1-10^{-n}}{9})=\frac{7}{81}(9n-1+10^{-n})$.
Correct Answer: 2