What's the Maximum

Algebra Level 3

Let S be a sequence whose first few terms are as follows: $\frac{1}{503} , \frac{4}{524} , \frac{9}{581} , \frac{16}{692}, \ldots, \frac{n^2}{500 + 3n^3 } , \ldots$

The largest term of the sequence can be expressed as $\frac{N}{M}$

Find the value of $M-N$ .

The answer is 1480.

2 solutions

Vyom Jain
Apr 16, 2015

the n'th term comes out to be differentiate it and equate to 0 to find the point of maxima which comes out to be nearly 7

and the 7 term is

hence the difference is 1480

Shohag Hossen
Jul 7, 2015

First 10 term's are , 1/503 , 4/524 , 9/581 , 16/692 , 25/875 , 36/1148 , 49/1529 , 64/2036 , 81/2687 , 100/3500.

Here , first < second < third < forth < fifth < sixth < seventh but after seventh , 7 th > 8 th > 9 th > 10 th > ..................... etc.

For this reason , 49/1529 is the largest term of the sequence .

So , M = 1529 , N = 49 .

M-N = 1480 .

What's the Maximum

The answer is 1480.

2 solutions

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