Sum of series Step by Step

You specify an expression under the sign sigma, the first member, the last member, or infinity if you need to find the limit of the sum.

Finds partial sums
The limit of the sum of the series
Convergence tests:
- Divergence
- Absolute convergence. Convergent series
- Conditional convergence
- Uniform convergence
- Necessary condition for convergence
- Leibniz criterion
- Weierstrass's Convergence Test
- Abel's criterion
- Dirichlet's test
- Limit comparison test
- Limit comparison test
- Cauchy condensation test
- Integral test for convergence
- Direct comparison test
- Raabe's Test
Supports:
- Function series:
  With variables x and z
  - Power series
  - Taylor series
  - Maclaurin series
  - Fourier series
  - Trigonometric series
  - Laurent series
- Alternating series / Alternating series
- Basel problem
- Harmonic series
- Grandi's series
- Flint Hills Series
- Kempner series
- Convergent series
- Divergent series
- Positive Series
- Partial series
- Other
Finds:
- Sum of series
- Numerical result of the sum
- The rate of convergence of the series
- The radius of convergence of the power series
Graphing:
- Partial sums
- The limit of the series

Learn more about Sum of series.

The above examples also contain:

the modulus or absolute value: absolute(x) or |x|
square roots sqrt(x),
cubic roots cbrt(x)
trigonometric functions:
sinus sin(x), cosine cos(x), tangent tan(x), cotangent ctan(x)
exponential functions and exponents exp(x)
inverse trigonometric functions:
arcsine asin(x), arccosine acos(x), arctangent atan(x), arccotangent acot(x)
natural logarithms ln(x),
decimal logarithms log(x)
hyperbolic functions:
hyperbolic sine sh(x), hyperbolic cosine ch(x), hyperbolic tangent and cotangent tanh(x), ctanh(x)
inverse hyperbolic functions:
hyperbolic arcsine asinh(x), hyperbolic arccosinus acosh(x), hyperbolic arctangent atanh(x), hyperbolic arccotangent acoth(x)
other trigonometry and hyperbolic functions:
secant sec(x), cosecant csc(x), arcsecant asec(x), arccosecant acsc(x), hyperbolic secant sech(x), hyperbolic cosecant csch(x), hyperbolic arcsecant asech(x), hyperbolic arccosecant acsch(x)
rounding functions:
round down floor(x), round up ceiling(x)
the sign of a number:
sign(x)
for probability theory:
the error function erf(x) (integral of probability), Laplace function laplace(x)
Factorial of x:
x! or factorial(x)
Gamma function gamma(x)
Lambert's function LambertW(x)
Trigonometric integrals: Si(x), Ci(x), Shi(x), Chi(x)

The following operations can be performed