Prove by mathematical induction that 7^(2n) - 48n - 1 is a multiple of 2304
I am ok with the first and second steps, but I am confused with the third i.e. when substituting n = k + 1.
Any help please?
Thanks a lot
hi yobacul,
F(n)
is a multiple 2304 ?
F(k+1)
is a multiple of 2304 if the "k"th term is ?
Does the hypothesis F(n) cause this to be true ?
Now express -48k as a multiple of
To do this we need to subtract another 48(48k)
{and therefore also add that amount}
The final term is
therefore, the term-by-term link is established.
Hence, if F(n) is valid, F(n+1) also is