ʰᵉʳᵉ ⁱˢ ᵒⁿᵉ ᵖᵒˢˢⁱᵇˡᵉ ʷᵃʸ ᵒᶠ ᵗʰⁱⁿᵏⁱⁿᵍ ᵃᵇᵒᵘᵗ ᵖᵒʷᵉʳˢ ᵒᶠ ²:

March 20, 2026Mathematics

ScanSolve AI Answer

Answer

2^{n} - 1

3 steps

Let $S$ be the sum of the first $n$ powers of 2, starting from $2^0$ .
$S = 1 + 2 + 4 + \dots + 2^{n-1}$
Multiply $S$ by 2 to shift the terms.
$2S = 2 + 4 + 8 + \dots + 2^n$
Subtract the original $S$ from $2S$ .
$2S - S = (2 + 4 + 8 + \dots + 2^n) - (1 + 2 + 4 + \dots + 2^{n-1})$ $S = 2^n - 1$
The sum is $\boxed{2^{n} - 1}$ .

Was this helpful?

A new problem that tests the same skill.

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question