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(1×(((1)/(2))^(n)-1))/(((1)/(2)-1))

(1×((12)n−1))/((12)−1)\left(1\times\left(\left(\frac{1}{2}\right)^n-1\right)\right)\bigg/\left(\left(\frac{1}{2}\right)-1\right)

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Evaluate definite integrals using the chain ruleright chevron icon

Full solution

Q. (1×((12)n−1))/((12)−1)\left(1\times\left(\left(\frac{1}{2}\right)^n-1\right)\right)\bigg/\left(\left(\frac{1}{2}\right)-1\right)
  1. Perform Subtraction in Denominator: Now, let's perform the subtraction in the denominator: (12−22)=−12(\frac{1}{2} - \frac{2}{2}) = -\frac{1}{2}.
  2. Simplify Expression by Division: Next, we can simplify the expression by dividing the numerator by the denominator. Since dividing by a negative is the same as multiplying by its reciprocal, we have (1×((12)n−1))/(−12)=−2×((12)n−1)(1\times\left(\left(\frac{1}{2}\right)^n-1\right))/(-\frac{1}{2}) = -2 \times \left(\left(\frac{1}{2}\right)^n - 1\right).
  3. Distribute −2-2 Across Terms: We can distribute the −2-2 across the terms in the parentheses to get −2×((12)n)+2-2 \times \left(\left(\frac{1}{2}\right)^n\right) + 2.
  4. Final Simplified Form: The expression is now simplified to −2×((12)n)+2-2 \times \left(\left(\frac{1}{2}\right)^n\right) + 2. This is the final simplified form of the given expression.

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