theorem Th58:
  seq is summable implies for n holds seq^\n is summable
proof
  assume
A1: seq is summable;
    let n;
A2: Re (seq^\n)=Re seq^\n & Im(seq^\n)=Im seq^\n by Th23;
    Re seq^\n is summable & Im seq^\n is summable by A1,SERIES_1:12;
    hence seq^\n is summable by A2,Th57;
end;
