Calculate infinite series, test convergence with step-by-step solutions and convergence tests.
Use n for the term number
∑arⁿ converges if |r| < 1
Sum = a/(1-r) when convergent
If lim aₙ ≠ 0, series diverges
Necessary but not sufficient
If 0 ≤ aₙ ≤ bₙ and ∑bₙ converges
Then ∑aₙ converges
If lim |aₙ₊₁/aₙ| = L
L < 1: converges, L > 1: diverges
If lim ⁿ√|aₙ| = L
If f(n) = aₙ and f is positive, decreasing
∫f(x)dx converges ⇔ ∑aₙ converges
a = 1, r = 0.5
a₁ = 1, d = 2, n = 10
aₙ = 1/n²
aₙ = 1/n
A series is the sum of the terms of a sequence. Infinite series continue indefinitely, while finite series have a specific number of terms.