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

Sum online

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`.
The sum function 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).

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

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.
- 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.
- Sequence calculator : sequence. Sequence calculator allows to calculate online the terms of the sequence whose index is between two limits.
- 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.