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Calculus · Series-And-Sums

Sum 3^k for k = 0 to n

\sum_{k=0}^{n} 3^{k}

Step by step

  1. \sum_{k=0}^{n} 3^{k}

    Write the sum out.

  2. 1 + 3 + 9 + 27 + \cdots

    The first few terms.

  3. = \frac{3 \cdot 3^{n} - 1}{2}

    Closed form (a standard summation formula, provable by induction).

Reveal the answer
\frac{3 \cdot 3^{n} - 1}{2}