Series & Sequences Calculator | AllScienceTools

Arithmetic (Add d)

a_n = a₁ + (n-1)d

S_n = n/2 (a₁ + a_n)

Geometric (Mult r)

a_n = a₁ · r^(n-1)

S_n = a₁(1-r^n) / (1-r)

S_∞ = a₁ / (1-r) (|r|<1)

Taylor (at a):
Σ fⁿ(a)/n! · (x-a)ⁿ

Maclaurin (at 0):
eˣ = 1 + x + x²/2! + ...
sin x = x - x³/3! + ...
cos x = 1 - x²/2! + ...
1/(1-x) = 1 + x + x² ...

Nth Term

Div if lim a_n ≠ 0

Ratio Test

L = |a_{n+1}/a_n|
Conv if L < 1

Root Test

L = ⁿ√|a_n|
Conv if L < 1

P-Series

1/nᵖ
Conv if p > 1

Preparing your Lab

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