# [racket] Puzzled with tail-recursion conversion

Hello, this is not really racket-related, for I get same issue with
larceny, for instance. I saw a function at reddit and tried reworking
it into tail-recursion, but it baffles me why last version shouldn't
work.
; original function: works
(define pi
(lambda (accuracy)
(letrec ((helper
(lambda (k accuracy)
(let ((this (* (/ (expt -1 k) (expt 4 k))
(+ (/ 2 (+ (* 4 k) 1))
(/ 2 (+ (* 4 k) 2))
(/ 1 (+ (* 4 k) 3))))))
(if (< (abs this) accuracy)
this
(+ this (helper (+ k 1) accuracy)))))))
(helper 0 accuracy))))
; more conventional define, removed redundant accuracy parameter in
helper and defined formula: works
(define (pi2 accuracy)
(define (formula k)
(* (/ (expt -1 k) (expt 4 k))
(+ (/ 2 (+ (* 4 k) 1))
(/ 2 (+ (* 4 k) 2))
(/ 1 (+ (* 4 k) 3)))))
(letrec ((helper
(lambda (k)
(let ((this (formula k)))
(if (< (abs this) accuracy)
this
(+ this (helper (+ k 1))))))))
(helper 0)))
; got rid of letrec and used named let: works
(define (pi3 accuracy)
(define (formula k)
(* (/ (expt -1 k) (expt 4 k))
(+ (/ 2 (+ (* 4 k) 1))
(/ 2 (+ (* 4 k) 2))
(/ 1 (+ (* 4 k) 3)))))
(let helper ((k 0))
(let ((this (formula k)))
(if (< (abs this) accuracy)
this
(+ this (helper (+ k 1)))))))
; reworked helper to get 1 extra parameter so that it's now
tail-recursive: doesn't work. It simply hangs in there
indefinitely...
(define (pi4 accuracy)
(define (formula k)
(* (/ (expt -1 k) (expt 4 k))
(+ (/ 2 (+ (* 4 k) 1))
(/ 2 (+ (* 4 k) 2))
(/ 1 (+ (* 4 k) 3)))))
(let helper ((k 1) (this (formula 0)))
(if (< (abs this) accuracy)
this
(helper (+ k 1) (+ this (formula k))))))
; any ideas?