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Sequences and series

Arithmetic and geometric sequences, partial sums, and the geometric series formula.

An arithmetic sequence adds the same amount each step; a geometric one multiplies by the same ratio. Their sums have closed forms — n(a₁ + aₙ)/2 and a(rⁿ − 1)/(r − 1) — and when |r| < 1 the geometric series keeps converging as n grows, which is the first infinite sum most people meet.

କାର୍ଯ୍ୟକାରୀ ଉଦାହରଣ: sum of 2^k for k = 0 to 10

Calculus · Series-And-Sums

Sum 2^k for k = 0 to 10

\sum_{k=0}^{10} 2^{k}

ପଦକ୍ଷେପ କ୍ରମେ

  1. \sum_{k=0}^{10} 2^{k}

    Write the sum out.

  2. = 2047

    Closed form.

ଉତ୍ତରକୁ ଖୋଲନ୍ତୁ
2047

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ଅଧିକ Precalculus

Complex numbersPolynomial functionsRational functionsThe binomial theoremConic sectionsVectors