# Sum of series Step by Step

= ### What can the sum of the series calculator do?

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

• 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

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 insertion rules

The following operations can be performed

2*x
- multiplication
3/x
- division
x^2
- squaring
x^3
- cubing
x^5
- raising to the power
x + 7
x - 6
- subtraction
Real numbers
insert as 7.5, no 7,5

#### Constants

pi
- number Pi
e
- the base of natural logarithm
i
- complex number
oo
- symbol of infinity