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Find Formulas for Definite Sums
Find a formula for a sequence of definite sums.
In[1]:=

Click for copyable input
Table[\!\(

\*UnderoverscriptBox[\(\[Sum]\), \(m\), \(10\)]

\*FractionBox[

SuperscriptBox[\(m\), \(n\)], \(m + 1\)]\), {n, 20}]
Out[1]=



In[2]:=

Click for copyable input
Table[\!\(

\*UnderoverscriptBox[\(\[Sum]\), \(m\), \(10\)]

\*FractionBox[

SuperscriptBox[\(m\), \(n\)], \(m + 1\)]\), {n, 20}];

FindSequenceFunction[%, n]
Out[2]=



In[3]:=

Click for copyable input
Table[\!\(

\*UnderoverscriptBox[\(\[Sum]\), \(m\), \(10\)]

\*FractionBox[

SuperscriptBox[\(m\), \(n\)], \(m + 1\)]\), {n, 20}];

FindSequenceFunction[%, n];

Table[\!\(

\*UnderoverscriptBox[\(\[Sum]\), \(m\), \(10\)]

\*FractionBox[

SuperscriptBox[\(m\), \(n\)], \(m + 1\)]\), {n, 100}] - 

 Table[%, {n, 100}]
Out[3]=