Compute the Limit of a Recursive Sequence

Recursive sequences of the form may be viewed as discrete dynamical systems. The limit (fixed point) of such a dynamical system can be computed directly using RSolveValue, as illustrated in the following.

Compute the limit of a linear recursive sequence.

In[1]:=1

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Out[1]=1

In[2]:=2

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Out[2]=2

Visualize the convergence of the sequence to its limiting value.

In[3]:=3

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Out[3]=3

The nested radical may be regarded as the limit of a nonlinear recursive sequence.

In[4]:=4

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Out[4]=4

Compute the exact value of the nested radical.

In[5]:=5

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Out[5]=5

The equation can be solved by computing the limit of the following trigonometric recursive sequence.

In[6]:=6

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Out[6]=6

Calculate the limit to an arbitrary precision.

In[7]:=7

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Out[7]=7

Visualize the convergence of the sequence to its limiting value.

In[8]:=8

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Out[8]=8