- #1
timothychoi
- 5
- 0
Hello. In the Wiki entry for "Leibniz harmonic triangle" there one
can find a formula
L(r, c) = 1/(c * binom(r - 1, c - 1))
where L(r, c) is the entry in the harmonic triangle and the
binom() is the usual binomial notation (or the entry from
Pascal triangle). I tried to prove the assertion using indunction
on n, then I was not able to finish. Can someone prove
the assertion using induction on n? Only the last step, that
is assuming that
L(k, c) = 1/(c * binom(k - 1, c - 1))
and showing that
L(k + 1, c) = 1/(c * binom((k + 1) - 1, c - 1)),
will be sufficient. Thank you.
can find a formula
L(r, c) = 1/(c * binom(r - 1, c - 1))
where L(r, c) is the entry in the harmonic triangle and the
binom() is the usual binomial notation (or the entry from
Pascal triangle). I tried to prove the assertion using indunction
on n, then I was not able to finish. Can someone prove
the assertion using induction on n? Only the last step, that
is assuming that
L(k, c) = 1/(c * binom(k - 1, c - 1))
and showing that
L(k + 1, c) = 1/(c * binom((k + 1) - 1, c - 1)),
will be sufficient. Thank you.