Sum of Series Calculator

Calculate the sum of arithmetic or geometric series with partial sums and step-by-step solutions.

Select Series Type & Enter Values

Result

Sum of Series
164

Step-by-Step Solution

Partial Sums

Understanding Series

A series is the sum of the terms of a sequence. The two most common types are arithmetic series (constant difference between terms) and geometric series (constant ratio between terms). Series appear throughout mathematics, physics, finance, and computer science.

Series Formulas

Arithmetic Series

Sum of terms with a constant difference d between consecutive terms.

S = n/2 x (2a + (n-1)d)

Geometric Series (r != 1)

Sum of terms with a constant ratio r between consecutive terms.

S = a(r^n - 1) / (r - 1)

Infinite Geometric (|r| < 1)

When the ratio is between -1 and 1, the infinite series converges.

S = a / (1 - r)

Applications

  • Compound interest calculations use geometric series.
  • Fourier series decompose signals into frequency components.
  • Taylor series approximate functions in calculus.
  • Partial sums are used in numerical analysis and convergence testing.