Recursive sequence calculator : How to use it?
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.
Syntax :
recursive_sequence(expression;first_term;upper bound;variable)
Examples :
This example shows how to calculate the first terms of a geometric sequence defined by recurrence. `u_(n+1)=4*u_n` and `u_0=-1` recursive_sequence(`4*x;-1;3;x`)
The calculator is able to calculate online the terms of a sequence defined by recurrence between two of the indices of this sequence.
It is also possible to calculate the elements of a numerical sequence when it is explicitly defined .
Calculation of the terms of a sequence defined by recurrence
The calculator is able to calculate the terms of a sequence defined by recurrence between two indices of this sequence.
Thus, to obtain the elements of a sequence defined by `u_(n+1)=5*u_n` and `u_0=2`, between 1 and 4 , enter : recursive_sequence(`5x;2;4;x`) after calculation, the result is returned.
Calculation of elements of an arithmetic sequence defined by recurrence
The calculator is able to calculate the terms of an arithmetic sequence between two indices of this sequence , from the first term of the sequence and a recurrence relation.
Thus, to obtain the terms of an arithmetic sequence defined by recurrence with the relation `u_(n+1)=5*u_n` et `u_0=3`, between 1 and 6 enter : recursive_sequence(`5*x;3;6;x`) after calculation, the result is returned.
Calculation of the terms of a geometric sequence
The calculator is able to calculate the terms of a geometric sequence between two indices of this sequence, from a relation of recurrence and the first term of the sequence.
Thus, to obtain the terms of a geometric sequence defined by `u_(n+1)=3*u_n` and `u_0=2`, between 1 and 4 , enter : recursive_sequence(`3*x;1;4;x`) after calculation, the result is returned.
Calculation of the sum of the terms of a sequence
The calculator is able to calculate the sum of the terms of a sequence between two indices of this series, it can be used in particular to calculate the partial sums of some series. .
- 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.
- 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.
- Sequence calculator : sequence. Sequence calculator allows to calculate online the terms of the sequence whose index is between two limits.
- 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.