
theorem Th13:
  for b be Nat st b > 1 holds Sum ((1/b) GeoSeq) = b/(b-1)
  proof
    let b be Nat;
    assume
A0: b > 1; then
A1: |. 1/b .| < 1 by Th9;
    Sum ((1/b) GeoSeq) = 1/( 1-(1/b) ) by A1,SERIES_1:24
 .= 1/( (b/b)-(1/b) ) by XCMPLX_1:60,A0
 .= 1/((b-1)/b) by XCMPLX_1:120
 .= b/(b-1) by XCMPLX_1:57;
    hence thesis;
  end;
