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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.

Ví dụ đã làm: `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}

Bước một bước

\sum_{k=0}^{10} 2^{k}
Write the sum out.
= 2047
Closed form.

Giải đáp

2047

Thử đi.

More in Precalculus

Complex numbers Polynomial functions Rational functions The binomial theorem Conic sections Vectors

Ví dụ đã làm: sum of 2^k for k = 0 to 10

Sum 2^k for k = 0 to 10

Bước một bước

Thử đi.

More in Precalculus

Ví dụ đã làm: `sum of 2^k for k = 0 to 10`