SumT
SumT[1, m]
is the alternative harmonic number ∑i=1m(−1)∧i/i
SumT[r, n]
represents Sum[(-1)^i/i^r, {i,1,n}]
SumT[r,s, n]
is Sum[1/k^r (-1)^j/j^s, {k, 1, n}, {j, 1, k}]
.
See also
Overview, SumP, SumS.
Examples
S~1(m−1)
S~2(m−1)
S~1(m)
SumT[1, m, Reduce -> True]
S~1(m−1)+m(−1)m
−127
S~12(m−1)
−1051212166070237840531600496448376108087919052800000038987958697055013360489864298703621429610152138683927
−127
−127
−2130000364800057561743656913
−1051212166070237840531600496448376108087919052800000038987958697055013360489864298703621429610152138683927
{−1,−85,−216179,−17281207,−216000170603,−216000155903}
Array[SumS[-2, 1, #1] &, 6]
{−1,−85,−216179,−17281207,−216000170603,−216000155903}