Series Sum Calculator

Calculate the sum of arithmetic, geometric, harmonic, and other series.

Series Type

First Term (a)

Common Difference (d)

Number of Terms (n)

100

S = n/2 × (a + l) = 10/2 × (1 + 19) = 100

135791113151719

nth Term: 19

Number of Terms: 10

Arithmetic Series

S = n/2 × (2a + (n-1)d)

S = n/2 × (a + l)

Geometric Series

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

S_inf = a/(1 - r) for |r| < 1

Harmonic Series

H_n = 1 + 1/2 + ... + 1/n

Diverges as n → ∞

P-Series

Σ(1/n^p)

Converges for p > 1