HELP!!!!!! induction question (1 Viewer)

[Trying to be a scholar]

Can someone help me with this induction question I'm so lost

Let H(n) = . Use mathematical induction to prove that for all positive integers n ≥ 1,

n + H(1) + H(2) + H(3) + … + H(n – 1) =nH(n).

 

[tito981]

im assuming you got up to proving for K+1 and you got up to:

kH(k)+1+H(k) after you plug in the assumption to LHS of the statement for n=k+1

then factor as such:

H(k)[k+1]+1

then factor out (k+1)

[k+1](H(k)+1/(k+1))

then note H(k) + 1/(k+1) = H(k+1)

thus you get [k+1]H(k+1) as required for n=k+1

(sorry i dont know how to type in latex yet)

 

[Trying to be a scholar]

im assuming you got up to proving for K+1 and you got up to:

kH(k)+1+H(k) after you plug in the assumption to LHS of the statement for n=k+1

then factor as such:

H(k)[k+1]+1

then factor out (k+1)

[k+1](H(k)+1/(k+1))

then note H(k) + 1/(k+1) = H(k+1)

thus you get [k+1]H(k+1) as required for n=k+1

(sorry i dont know how to type in latex yet)

THANKYOUUUUU so muchhhhhh