Sequence-And-Series Question 675
Question: The sum to n terms of the series $ \frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+………. $ is
Options:
A) $ n-1-{2^{-n}} $
B) 1
C) $ n-1+{2^{-n}} $
D) $ 1+{2^{-n}} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ \frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+…. $ $ =( 1-\frac{1}{2} )+( 1-\frac{1}{4} )+( 1-\frac{1}{8} )+( 1-\frac{1}{16} )+… $ $ =n-\frac{\frac{1}{2}{ 1-\frac{1}{2^{n}} }}{1-\frac{1}{2}}=n-1+{2^{-n}} $
BETA
