Lodz697 wrote:
A sequence 1, 1/2, 1/4, ...,\(a_n\) is such that\(a_n=\frac{1}{2}*a_{n-1}\) , then which of the following is true about\(a_{10}\) ?
(A)\( 0.01 < a_{10} <0.1\)
(B)\( 0.001 < a_{10} <0.01\)
(C)\( 0.0001 < a_{10} <0.001\)
(D)\( 0.00001 < a_{10} <0.0001\)
(E)\( 0.000001 < a_{10} <0.00001\)
Why the answer is not C?
If 1/1000 = 0,001, 1/1024 must be smaller than 0,001...
Where am Iwrong?
Bunuel
\(a_1=\frac{1}{2^0}=1\),
\(a_2=\frac{1}{2^1}=\frac{1}{2}\),
\(a_3=\frac{1}{2^2}=\frac{1}{4}\),
\(a_4=\frac{1}{2^3}=\frac{1}{8}\),
...
\(a_n=\frac{1}{2^{n-1}}\).
Hence,\(a_{10}\) isnot \(\frac{1}{2^{10}}=\frac{1}{1,024}\) ,it's \(\frac{1}{2^{9}}=\frac{1}{512}=\frac{2}{1,024} \) , which is a bit less than 0.002, making B the answer.
Holpe it helps.
...
Statistics : Posted by Bunuel • on 21 Jan 2021, 22:51 • Replies 5 • Views 1427
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