This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Documentation / Mathematica / Built-in Functions / Numerical Computation / Sums and Products /

Further Examples: Sum

Here is the sum of the first odd integers.

In[1]:=

Out[1]=

Here is another finite sum.

In[2]:=

Out[2]=

This makes the iterator increment in steps of .

In[3]:=

Out[3]=

Here is a triangular array.

In[4]:=

Out[4]//TableForm=

Here is its sum.

In[5]:=

Out[5]=

Mathematica gives an exact result for this sum.

In[6]:=

Out[6]=

Wrapping N around this result gives a numerical approximation.

In[7]:=

Out[7]=

If you know that you need a numerical result from the start, NSum is faster.

In[8]:=

Out[8]=

Symbolic sums

In[9]:=

Out[9]=

In[10]:=

Out[10]=

In[11]:=

Out[11]=

In[12]:=

Out[12]=

In[13]:=

Out[13]=

In[14]:=

Out[14]=

In[15]:=

Out[15]=

Infinite series whose sums contain

In[16]:=

Out[16]=

In[17]:=

Out[17]=

In[18]:=

Out[18]=

In[19]:=

Out[19]=

In[20]:=

Out[20]=

In[21]:=

Out[21]=

In[22]:=

Out[22]=

In[23]:=

Out[23]=

In[24]:=

Out[24]=

In[25]:=

Out[25]=

In[26]:=

Out[26]=

In[27]:=

Out[27]=

In[28]:=

Out[28]=

In[29]:=

Out[29]=

Other infinite series

In[30]:=

Out[30]=

In[31]:=

Out[31]=

In[32]:=

Out[32]=

In[33]:=

Out[33]=

In[34]:=

Out[34]=

In[35]:=

Out[35]=

In[36]:=

Out[36]=

In[37]:=

Out[37]=

In[38]:=

Out[38]=

In[39]:=

Out[39]=