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# Help is needed!

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What is the following value when expressed as a common fraction:
$$\frac{1}{2^{1}}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+\cdots + \frac{1}{2^{8}}+\frac{1}{2^{9}}+\frac{1}{2^{10}}?$$

Sorry that the question looks weird!

Aug 16, 2020

#2
+30931
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What is the following value when expressed as a common fraction:
$$\frac{1}{2^{1}}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+\cdots + \frac{1}{2^{8}}+\frac{1}{2^{9}}+\frac{1}{2^{10}}$$?

$$\frac{1}{2^{1}}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+\cdots + \frac{1}{2^{8}}+\frac{1}{2^{9}}+\frac{1}{2^{10}}=\frac{2^9+2^8+2^7+...+2^2+2+1}{2^{10}} =\frac{512+256+128+...+4+2+1}{1024}=\frac{1023}{1024}$$

Aug 16, 2020