Evaluate New Classes of Telescoping Sums and Products 

Evaluate an indefinite sum using functional telescoping.

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X expr = 2^k/(3^k - 2^k);

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X expr1 = DifferenceDelta[expr, k]

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In[3]:=

X Sum[expr1, k]

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Sum the expression on finite and infinite intervals.

In[4]:=

X Sum[expr1, {k, 1, n}]

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In[5]:=

X Sum[expr1, {k, 1, \[Infinity]}]

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Evaluate an indefinite product using functional telescoping.

In[6]:=

X expr = (Cos[b + a (((-1 + a^k) b)/(-1 + a) + a^k x)]^( b + a (((-1 + a^k) b)/(-1 + a) + a^k x)) + Sin[b + a (((-1 + a^k) b)/(-1 + a) + a^k x)])/( Cos[((-1 + a^k) b)/(-1 + a) + a^k x]^(((-1 + a^k) b)/(-1 + a) + a^k x) + Sin[((-1 + a^k) b)/(-1 + a) + a^k x]);

In[7]:=

X Product[expr, k]

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