# Has zero a value before the decimal point

## Sum of the terms of a sequence

#### Summary :

With the summation calculator you can calculate online the sum of the terms in the sequence whose index is between the lower and upper limit.

sum online#### Description :

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

### Calculation of the sum of the terms of a number sequence

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

For example, to get 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.

### Calculation of the sum of the terms of a sequence

The calculator is capable of that **Sum of the terms of a sequence** between two indices of this sequence.

So to the **Sum of terms** To get a sequence defined by `u_n = n ^ 2` between 1 and 4, you have to enter: sum (` n; 1; 4; n ^ 2`). After the calculation, the result 30 is returned (`sum_ (n = 1) ^ 4 n ^ 2 = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 = 30`).

### Calculation of the sum of the terms of an arithmetic sequence

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

With this formula the calculator is able to calculate the **Sum of the terms in an arithmetic sequence** to determine between two indices of this sequence.

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

The calculator can find the general formula that allows it to calculate the sum of the whole numbers: `1 + ... + p = p * (p + 1) / 2`, just type: sum (` n; 1 ; p; n`) a.

With this formula the calculator can e.g. calculate the sum of the whole numbers between 1 and 100: `S = 1 + 2 + 3 + ... + 100`.

To find this math sum, just type: sum (`n; 1; 100; n`).

### Calculation of the sum of the terms of a geometric sequence

**The sum of the terms of a geometric sequence** `u_n` between the indices p and n results from 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 that **Sum of the terms of a geometric sequence** between two indices of this sequence.

So to the **Sum of the terms of a geometric sequence** which is defined by: `u_n = 3 * 2 ^ n` between 1 and 4, you have to enter: sum (` n; 1; 4; 3 * 2 ^ n`). After the calculation, the result is returned.

### Numerical and vectorial series calculator

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

Either the series `sum (3 + 5 * n)`, the series calculator allows you to calculate the terms of the sequence of its partial sums, which are given by: `U_n = sum_ (k = 0) ^ n (3 + 5 * k ) '. So to calculate: `U_5 = sum_ (k = 0) ^ 5 (3 + 5 * k)`, you need to sum (`k; 0; 5; 3 + 5 * k`).

With the summation calculator you can calculate online the sum of the terms in the sequence whose index is between the lower and upper limit.

#### Syntax:

sum (index; lower limit; upper limit; sequence)#### Examples:

sum (`n; 1; 4; n ^ 2`), 30 returns (30 =` 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2`). Calculate online with sum (sum of the terms of a sequence)- What is the range of a LAN
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