Aim of the applet

Representation of numerical series.

Input data

The user defines the series of numbers to represent and limits.

Output data

Representation of the numerical series

Representation of the partial sum

Sum of k terms of the series.

Representation of series convergence

Observations

The user can select which output data display.

You can adjust the graphical view to the series or to the series and partial sum.

Convergence criterion:

-If convergence tends below 1 converges.

-If convergence tends to one does not decide.

-If convergence tends above 1 does not converge.

The first steps

• Find the general term of the series 1 + 1 / 2 + 1 / 4 + 1 / 8 + ... Calculate the sum of the first 10 terms and with the mouse changes k to always display the same value of the sum, what is?
• Calculate the sum of the first terms of the series whose general term is n / (n +1). As you can see the sequence does not approximate to zero. Besides, increasing k we don't see approximate to a fixed number the partial sum.
• Write an alternating series (the sign is changing) so that the sum of terms is close to a value.