Solve 4又1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256

Question

Simplify the expression

2 Y o u + \frac{127}{256}

Evaluate

\frac{4 Y o u \times 1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128} + \frac{1}{256}

Reduce the fraction

More Steps

2 Y o u + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128} + \frac{1}{256}

Solution

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Evaluate

\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128} + \frac{1}{256}

Reduce fractions to a common denominator

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{4 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} + \frac{2 \times 2 \times 2 \times 2 \times 2}{8 \times 2 \times 2 \times 2 \times 2 \times 2} + \frac{2 \times 2 \times 2 \times 2}{16 \times 2 \times 2 \times 2 \times 2} + \frac{2 \times 2 \times 2}{32 \times 2 \times 2 \times 2} + \frac{2 \times 2}{64 \times 2 \times 2} + \frac{2}{128 \times 2} + \frac{1}{256}

Multiply the terms

More Steps

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2 \times 2}{8 \times 2 \times 2 \times 2 \times 2 \times 2} + \frac{2 \times 2 \times 2 \times 2}{16 \times 2 \times 2 \times 2 \times 2} + \frac{2 \times 2 \times 2}{32 \times 2 \times 2 \times 2} + \frac{2 \times 2}{64 \times 2 \times 2} + \frac{2}{128 \times 2} + \frac{1}{256}

Multiply the terms

More Steps

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2}{16 \times 2 \times 2 \times 2 \times 2} + \frac{2 \times 2 \times 2}{32 \times 2 \times 2 \times 2} + \frac{2 \times 2}{64 \times 2 \times 2} + \frac{2}{128 \times 2} + \frac{1}{256}

Multiply the terms

More Steps

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2}{32 \times 2 \times 2 \times 2} + \frac{2 \times 2}{64 \times 2 \times 2} + \frac{2}{128 \times 2} + \frac{1}{256}

Multiply the terms

More Steps

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2}{256} + \frac{2 \times 2}{64 \times 2 \times 2} + \frac{2}{128 \times 2} + \frac{1}{256}

Multiply the terms

More Steps

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2}{256} + \frac{2 \times 2}{256} + \frac{2}{128 \times 2} + \frac{1}{256}

Multiply the numbers

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2}{256} + \frac{2 \times 2}{256} + \frac{2}{256} + \frac{1}{256}

Write all numerators above the common denominator

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 + 2 \times 2 + 2 + 1}{256}

Multiply the terms

More Steps

\frac{64 + 2 \times 2 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 + 2 \times 2 + 2 + 1}{256}

Multiply the terms

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\frac{64 + 32 + 2 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 + 2 \times 2 + 2 + 1}{256}

Multiply the terms

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\frac{64 + 32 + 16 + 2 \times 2 \times 2 + 2 \times 2 + 2 + 1}{256}

Multiply the terms

More Steps

\frac{64 + 32 + 16 + 8 + 2 \times 2 + 2 + 1}{256}

Multiply the numbers

\frac{64 + 32 + 16 + 8 + 4 + 2 + 1}{256}

Add the numbers

\frac{127}{256}

2 Y o u + \frac{127}{256}

Show Solution

Factor the expression

\frac{1}{256} (512 Y o u + 127)

Evaluate

\frac{4 Y o u \times 1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128} + \frac{1}{256}

Any expression multiplied by 1 remains the same

\frac{4 Y o u}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128} + \frac{1}{256}

Divide the terms

More Steps

2 Y o u + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128} + \frac{1}{256}

Add the numbers

More Steps

Evaluate

\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128} + \frac{1}{256}

Reduce fractions to a common denominator

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{4 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} + \frac{2 \times 2 \times 2 \times 2 \times 2}{8 \times 2 \times 2 \times 2 \times 2 \times 2} + \frac{2 \times 2 \times 2 \times 2}{16 \times 2 \times 2 \times 2 \times 2} + \frac{2 \times 2 \times 2}{32 \times 2 \times 2 \times 2} + \frac{2 \times 2}{64 \times 2 \times 2} + \frac{2}{128 \times 2} + \frac{1}{256}

Multiply the terms

More Steps

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2 \times 2}{8 \times 2 \times 2 \times 2 \times 2 \times 2} + \frac{2 \times 2 \times 2 \times 2}{16 \times 2 \times 2 \times 2 \times 2} + \frac{2 \times 2 \times 2}{32 \times 2 \times 2 \times 2} + \frac{2 \times 2}{64 \times 2 \times 2} + \frac{2}{128 \times 2} + \frac{1}{256}

Multiply the terms

More Steps

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2}{16 \times 2 \times 2 \times 2 \times 2} + \frac{2 \times 2 \times 2}{32 \times 2 \times 2 \times 2} + \frac{2 \times 2}{64 \times 2 \times 2} + \frac{2}{128 \times 2} + \frac{1}{256}

Multiply the terms

More Steps

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2}{32 \times 2 \times 2 \times 2} + \frac{2 \times 2}{64 \times 2 \times 2} + \frac{2}{128 \times 2} + \frac{1}{256}

Multiply the terms

More Steps

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2}{256} + \frac{2 \times 2}{64 \times 2 \times 2} + \frac{2}{128 \times 2} + \frac{1}{256}

Multiply the terms

More Steps

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2}{256} + \frac{2 \times 2}{256} + \frac{2}{128 \times 2} + \frac{1}{256}

Multiply the numbers

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2 \times 2}{256} + \frac{2 \times 2 \times 2}{256} + \frac{2 \times 2}{256} + \frac{2}{256} + \frac{1}{256}

Write all numerators above the common denominator

\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 + 2 \times 2 + 2 + 1}{256}

Multiply the terms

More Steps

\frac{64 + 2 \times 2 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 + 2 \times 2 + 2 + 1}{256}

Multiply the terms

More Steps

\frac{64 + 32 + 2 \times 2 \times 2 \times 2 + 2 \times 2 \times 2 + 2 \times 2 + 2 + 1}{256}

Multiply the terms

More Steps

\frac{64 + 32 + 16 + 2 \times 2 \times 2 + 2 \times 2 + 2 + 1}{256}

Multiply the terms

More Steps

\frac{64 + 32 + 16 + 8 + 2 \times 2 + 2 + 1}{256}

Multiply the numbers

\frac{64 + 32 + 16 + 8 + 4 + 2 + 1}{256}

Add the numbers

\frac{127}{256}

2 Y o u + \frac{127}{256}

Solution

\frac{1}{256} (512 Y o u + 127)

Show Solution