# 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)