Series calculator allows to calculate online the sum of the terms of the sequence whose index is between the lower and the upper bound.

The calculator is able to **calculate online the sum of the terms of a sequence** between two indices of this sequence.

The calculator allows you to calculate a **sum of numbers**, just use the vector notation.

For example, to obtain the sum of the following list of numbers: 6;12;24;48, you must enter : sum(`[6;12;24;48]`). The result is then calculated in its exact form.

The calculator is able to calculate the **sum elements of a sequence** between two indices of this sequence.

To get the **sum elements of a sequence** defined by
`u_n=n^2` betwwen 1 and 4 , enter :
sum(`n;1;4;n^2`) after calculation, result 30 is given (`sum_(n=1)^4 n^2=1^2+2^2+3^2+4^2=30`).

**The sum of the terms of an arithmetic sequence** `u_n`, between the indices p and n, is given by the following **formula** :
`u_p+u_(p+1)+...+u_n=(n-p+1)*(u_p+u_n)/2`

Using this formula, the calculator is able to determine the **sum of the terms of an arithmetic sequence** between two indices of that sequence.

Thus, to obtain the **sum of the terms of an arithmetic sequence** defined by
`u_n=3+5*n` between 1 and 4 , you must enter :
sum(`n;1;4;3+5*n`),
after calculation, the result is returned.

The calculator is able to find the general formula that allows to calculate the sum of the integers:
`1+...+ p= p*(p+1)/2`, just enter :
sum(`n;1;p;n`).

The calculator can use this formula to, for example, calculate the sum of integers between 1 and 100:
`S=1+2+3+...+100`.

To calculate this sum, simply enter : sum(`n;1;100;n`).

**The sum of the terms of a geometric sequence** `u_n`, between the indices p and n, is given by the following **formula** :
`u_p+u_(p+1)+...+u_n=u_p*(1-q^(n-p+1))/(1-q)`, q is the reason for the sequence.

Thanks to this formula, the calculator is able to calculate the **sum of elements of an geometric sequence** between two indices
of this sequence.

To get the **sum elements of an geometric sequence** defined by
`u_n=3*2^n` between 1 and 4 , enter :
sum(`n;1;4;3*2^n`) after calculation, the result is given .

Let `u_n` a value sequence be in `RR` or `CC`, we call **series** of general term `U_n` the sequence defined by `U_n=sum_(k=0)^n u_n`,
for all `n in NN`.
This calculator can be used as a **series calculator**, to calculate the sequence of partial sums of a series.

With the series `sum (3+5*n)`, the series calculator makes it possible to calculate the terms of the sequence of its partial summaries defined by `U_n=sum_(k=0)^n (3+5*k)`. So to calculate `U_5=sum_(k=0)^5 (3+5*k)`, you have to enter sum(`k;0;5;3+5*k`).

sum(index;lower bound; upper bound;sequence)

sum(`n;1;4;n^2`), returns 30, ie `1^2+2^2+3^2+4^2`

See also

- Calculate product elements of sequence : product. Product function calculates online the product of the terms of the sequence whose index is between the lower and the upper bound.
- Calculate sum elements of sequence : sum. Series calculator allows to calculate online the sum of the terms of the sequence whose index is between the lower and the upper bound.
- Sequence calculator : sequence. Sequence calculator allows to calculate online the terms of the sequence whose index is between two limits.
- Recursive sequence calculator : recursive_sequence. The calculator of sequence makes it possible to calculate online the terms of the sequence, defined by recurrence and its first term, until the indicated index.