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In mathematics, the Nth harmonic number is defined to be 1 + 1/2 + 1/3 + 1/4 + ... + 1/N. So, the first harmonic number is 1, the second is 1.5, the third is 1.83333... and so on. Assume that n is an integer variable whose value is some positive integer N. Assume also that cl is a variable whose value is the Nth harmonic number. Write an expression whose value is the (N+1)th harmonic number.

Respuesta :

Answer:

cl   +   1/(N+1)

Step-by-step explanation:

If we assume that the Nth harmonic number is cl. Then we are assuming that 1+1/2+1/3+1/4+...+1/N=cl

And we know that the (N+1)th harmonic number can be found by doing

1+1/2+1/3+1/4+...+1/N+1/(N+1)

=cl    +   1/(N+1)

The (N+1)th harmonic number is cl   +   1/(N+1) given that the Nth term is cl

Other way to see the answers:

Maybe you want to write it as a single fraction so you have

[cl(N+1)+1]/(N+1)=[cl*N+cl+1]/(N+1)

The expression value is [tex]hn+(\frac{1}{n+1} )[/tex].

Assume that [tex]n[/tex] is an integer variable whose value is some positive integer [tex]N[/tex].

Assume also that [tex]hn[/tex] is a variable whose value is the [tex]N_{th} [/tex] harmonic number.

An expression whose value is the [tex](N+1)th[/tex] harmonic number is [tex]hn+(\frac{1}{n+1} )[/tex].

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