theorem Th49: :: CATALAN2:49

for seq1, seq2 being Real_Sequence
for n being Nat st seq2 is summable holds
ex Fr being XFinSequence of REAL st
( (Partial_Sums (seq1 (##) seq2)) . n = ((Sum seq2) * ((Partial_Sums seq1) . n)) - (Sum Fr) & dom Fr = n + 1 & ( for i being Nat st i in n + 1 holds
Fr . i = (seq1 . i) * (Sum (seq2 ^\ ((n -' i) + 1))) ) )