How to resolve the algorithm Harmonic series step by step in the BASIC programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Harmonic series step by step in the BASIC programming language

Table of Contents

Problem Statement

In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers: The series of harmonic numbers thus obtained is often loosely referred to as the harmonic series. Harmonic numbers are closely related to the Riemann zeta function, and roughly approximate the natural logarithm function; differing by γ (lowercase Gamma), the Euler–Mascheroni constant. The harmonic series is divergent, albeit quite slowly, and grows toward infinity.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Harmonic series step by step in the BASIC programming language

Source code in the basic programming language

h = 0.0

print "The first twenty harmonic numbers are:"
for n = 1 to 20
	h += 1.0 / n
	print n, h
next n
print

h = 1 : n = 2
for i = 2 to 10
	while h < i
		h += 1.0 / n
		n += 1
	end while
	print "The first harmonic number greater than "; i; " is "; h; ", at position "; n-1
next i
end

100 cls
110 print "The first twenty harmonic numbers are:"
120 for n = 1 to 20
130   h = h+(1/n)
140   print n,h
150 next n
160 print
170 h = 1
180 n = 2
190 for i = 2 to 10
200   while h < i
210     h = h+(1/n)
220     n = n+1
230   wend
240   print "The first harmonic number greater than ";i;"is ";h;" at position ";n-1
250 next i
260 end


precision 5

print "the first twenty harmonic numbers are:"

for n = 1 to 20

	let h = h + 1 / n
	print n, tab, h

next n

print newline, "the nth index of the first harmonic number that exceeds the nth integer:"

let h = 1
let n = 2

for i = 2 to 10

	do

		if h < i then

			let h = h + 1 / n
			let n = n + 1

		endif

		wait

	loop h < i

	print tab, n - 1,

next i


Public Sub Main() 
  
  Dim h As Float = 0
  Dim n As Integer, i As Integer
  
  Print "The first twenty harmonic numbers are:" 
  For n = 1 To 20 
    h += 1 / n 
    Print n, h 
  Next 
  Print 
  
  h = 1
  n = 2 
  For i = 2 To 10 
    While h < i 
      h += 1 / n 
      n += 1 
    Wend 
    Print "The first harmonic number greater than "; i; " is "; h; ", at position "; n - 1 
  Next
  
End


100 CLS : REM HOME 100 HOME for Applesoft BASIC
110 PRINT "The first twenty harmonic numbers are:"
120 FOR n = 1 TO 20
130   h = h+(1/n)
140   PRINT n,h
150 NEXT n
160 PRINT
170 h = 1
180 n = 2
190 FOR i = 2 TO 10
200   IF NOT(h < i) THEN GOTO 240
210     h = h+(1/n)
220     n = n+1
230   GOTO 200
240   PRINT "The first harmonic number greater than " i "is " h "at position " n-1
250 NEXT i
260 END


h = 0!

PRINT "The first twenty harmonic numbers are:"
FOR n = 1 TO 20
    h = h + 1! / n
    PRINT n, h
NEXT n
PRINT

h = 1: n = 2
FOR i = 2 TO 10
    WHILE h < i
        h = h + 1! / n
        n = n + 1
    WEND
    PRINT "The first harmonic number greater than "; i; " is "; h; ", at position "; n - 1
NEXT i
END


print "The first twenty harmonic numbers are:"
for n = 1 to 20
  h = h + 1 / n
  print n; chr$(9);h		' print n,h  for Just BASIC and Liberty BASIC
 next n
print
h = 1
n = 2
for i = 2 to 10
  while h < i
     h = h + 1 / n
     n = n +1
   wend
   print "The first harmonic number greater than ";i; " is ";h;" at position ";n-1
next i
end

LET h = 0

PRINT "The first twenty harmonic numbers are:"
FOR n = 1 TO 20
    LET h = h + 1 / n
    PRINT n, h
NEXT n
PRINT

LET h = 1
LET n = 2
FOR i = 2 TO 10
    DO WHILE h < i
       LET h = h + 1 / n
       LET n = n + 1
    LOOP
    PRINT "The first harmonic number greater than "; i; " is "; h; ", at position "; n - 1
NEXT i
END


h = 0.0

print "The first twenty harmonic numbers are:"
for n = 1 to 20
    h = h + 1.0 / n
    print n, chr$(9), h
next n
print

h = 1 : n = 2
for i = 2 to 10
    while h < i
        h = h + 1.0 / n
        n = n + 1
    wend
    print "The first harmonic number greater than ", i, " is ", h, ", at position ", n-1
next i
end

  

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