The number of terms of a harmonic sequence is even.

The sum of the terms in the odd places (First term + Third Term + Fifth Term + ...and so on) is 2625, and:
The sum of the terms in the even places (Second Term + Fourth Term + Sixth Term + ... and so on) is 4224; and:

Given that the last term exceeds the first by 2205, then identify the terms of the said sequence.

An increasing harmonic sequence must look like this:

                        k*{1/a_n, 1/a_n-1, 1/a_n-2,……………, 1/a₁}

where the a_i are in arithmetic progression and increasing with i.

I can’t believe that KS would expect us to ‘identify all the terms’
if there were more than, say, eight. Also, surely he would want
to keep things simple:

                        k*{1/8, 1/7, 1/6, …………, ½, 1}

His condition for the difference then gives 7k/8 = 2205 so that
k = 2520 and the terms are:

            {315, 360, 420, 504, 630, 840, 1260, 2520}

The other conditions seem to be satisfied!

Lateral thinking, or a retrospective view following an exhaustive
computer search? I’ll let you decide.

Posted by Harry on 2016-04-02 16:42:36