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Sum arithmetic and geometric series exactly, find the infinite sum of a converging geometric series, or add up any expression Σ f(k) between two limits.
Also covers: Partial sum calculator · Sum of arithmetic series · Geometric series sum · Sigma notation calculator · Summation calculator
Integers, decimals, or fractions like 1/2.
Up to 2,000.
S10 (sum of the first 10 terms)
1023/512
≈ 1.998046875
Last term a10
1/512
Infinite sum S∞
2
converges since |r| < 1
Terms
10
Working
Arithmetic or geometric for a sum from the first term, or Σ f(k) to add up any expression such as k² or 1/k².
Give the first term, the common difference or ratio, and how many terms; or the expression f(k) and the values of k to sum from and to.
Arithmetic and geometric sums are exact (fractions stay fractions), with the formula and working. A geometric series with |r| < 1 also shows its infinite sum.
Arithmetic: Sₙ = n(2a₁ + (n − 1)d) / 2. Geometric: Sₙ = a₁(1 − rⁿ) / (1 − r), or n · a₁ when r = 1.
Only when the common ratio is between −1 and 1. Then S∞ = a₁ / (1 − r); for example 1 + 1/2 + 1/4 + … = 2. Otherwise the series diverges.
It adds the terms one by one in floating point with compensated (Kahan) summation, accurate to about 12 significant digits, for up to a million terms.
No. Every calculation runs in your browser.
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