# calculate sum elements of sequence

Quizzes and games : numerical sequence

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

Quizzes and games : numerical sequence

### Sum, online calculus

#### Summary :

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

#### Description :

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

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

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.

## Sum calculation of terms of a sequence

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).

## Sum calculation of elements of an arithmetic sequence

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).

## Sum calculation of elements of a geometric sequence

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 .

## Series calculator

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).

#### Syntax :

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

#### Examples :

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

Calculate online with sum (calculate sum elements of sequence)