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Popular >

simplify 2(1-1/(2^k))

Solution

simplify

2 (1 - \frac{1}{2 ^{k}})

Solution

2^{1 - k} (2^{k} - 1)

Solution steps

2 (1 - \frac{1}{2 ^{k}})

Join

1 - \frac{1}{2 ^{k}} : \frac{2 ^{k} - 1}{2 ^{k}}

= 2 \cdot \frac{2 ^{k} - 1}{2 ^{k}}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 ( 2 ^{k} - 1 )}{2 ^{k}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{1}}{2 ^{k}} = 2^{1 - k}

= 2^{1 - k} (2^{k} - 1)

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Frequently Asked Questions (FAQ)

What is 2(1-1/(2^k)) ?
The solution to 2(1-1/(2^k)) is 2^{1-k}(2^k-1)