calculate sum elements of 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.

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`