# Summation Calculator (Sigma)

See guidelines and examples below.
input a single letter
to multiply, enter a*b and not ab
input oo (double o) for +infinity

Cet outil calcul la somme d'une suite de termes, notée comme suit,

\sum_{k=p}^{n} u_k = u_p + u_(p+1) + ... + u_(n-1) + u_n

• k is the sommation index,
• p et n are respectively the lower and upper range of the sommation, which means that the sum of the u_k terms begin from k=p and end at k=n.

## How to use this calculator ?

'index' field Input a single letter which denotes the sommation index. Example: i or k Expression (above u_i) to sum.this field may include a secondary variable, e.g. u_i = i + msee more details below. lower limit of the index range (denoted 'p' above). You may input a number or a secondary variable. upper limit of the index range (denoted 'n' ci-dessus). You may input a number or a secondary variable or oo (double o) for '+infinity' which is useful for infinite sum calculations.
Authorized expressions

Numbers : digits, fractions, decimal numbers (separator : dot)

Operators : + - * / ^ (power)
To multiply a by b, input a*b and not ab, e.g. 2*x.

Constants : pi, e

Functions
sqrt (square root), exp (exponential), log(x) or ln (natural logarithm), sin (sine), cos (cosine), tan (tangent), cot (cotangent), sec (secant), csc (cosecant), asin (arcsine), acos (arccosine), atan (arctangent), acot (arccotangent), asec (arcsecant), acsc (arccosecant) sinh (hyperbolic sine), cosh (hyperbolic cosine), tanh (hyperbolic tangent), coth (hyperbolic cotangent), sech (hyperbolic secant), csch (hyperbolic cosecant) asinh (Inverse hyperbolic sine) acosh (Inverse hyperbolic cosine), atanh (Inverse hyperbolic tangent), acoth (Inverse hyperbolic cotangent), asech (Inverse hyperbolic secant), acsch (Inverse hyperbolic cosecant)

## Sum Examples

Clic on an expression to see correspondant calculator.

• Sum of the first 100 natural numbers

1 + 2 + 3 + 4 + ... + 99 + 100 = 5050

• Sum of the first n natural numbers

1 + 2 + 3 + 4 + ... + n = (n*(n+1))/2

• Sum of squares of the first 100 natural numbers

12 + 22 + 32 + 42 + ... + 1002 = 338350

• Sum of squares of the first n natural numbers

1^2 + 2^2 + 3^2 + 4^2 + ... + n^2 = (n*(n+1)*(2n+1))/6

• Sum of inverse of the first n natural numbers

1 + 1/2 + 1/3 + 1/4 + ... + 1/(n-2) + 1/(n-1) + 1/n = H(n) (Harmonic series)

• Sum of inverse of natural numbers

1 + 1/2 + 1/3 + 1/4 + 1/5 ... = oo

• Sum of inverse of natural numbers with alternating sign

1/1 - 1/2 + 1/3 - 1/4 + 1/5 ... = log(2)

• Sum of inverse of odd natural numbers with alternating sign

1/1 - 1/3 + 1/5 - 1/7 + ... = pi/4

• Sum of first n even natural numbers

2 + 4 + 6 + ... + 2*(n-1) + 2*n = n*(n+1)

• Sum of first n odd natural numbers

1 + 3 + 5 + 7 + ... + (2n-1) = n^2

• Finite Sum of the Reciprocals of Powers of 2

1 + 1/2 + 1/2^2 + 1/3^2 + ... 1/2^n = 2*(1-1/2^(n+1))

• Infinite Sum of the Reciprocals of Powers of 2

1 + 1/2 + 1/2^2 + 1/3^2 + ... = 2