+285 What is the following value when expressed as a common fraction:
\(\frac{1}{2^{1}}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+\cdots + \frac{1}{2^{8}}+\frac{1}{2^{9}}+\frac{1}{2^{10}}?\)
+539 if we convert each number to make the denominator 2^10, we get 2^9+2^8...1(all the numerators).
If we add powers of 2 starting from one, it is always one less than the nest power of 2
1+2 is 1 less than 4, 1+2+4 is 1 less than 8, and so on.
So it would be (2^10-1)/2^10, or 1023/1024.
+539 if we convert each number to make the denominator 2^10, we get 2^9+2^8...1(all the numerators).
If we add powers of 2 starting from one, it is always one less than the nest power of 2
1+2 is 1 less than 4, 1+2+4 is 1 less than 8, and so on.
So it would be (2^10-1)/2^10, or 1023/1024.
