Mind-blowing Sequence.

Algebra Level 4

$\frac{1}{503},\frac{4}{524},\frac{9}{581},\frac{16}{692},\frac{25}{875}.......$

Find the largest term of the above sequence ?

\frac{4}{524}

\frac{16}{692}

\frac{49}{1529}

\frac{49}{1234}

1 solution

U Z
Oct 1, 2014

its an calculas based problem

$\huge{T_{n}}$ = $\huge{\frac{n^{2}}{500 + 3n^{3}}}$

then by differentiating and then keeping it to 0

we get $\huge{\frac{49}{1529}}$

Finding the General term of this sequence is quite interesting !!!

Sandeep Bhardwaj - 6 years, 8 months ago

sir what was your method

U Z - 6 years, 8 months ago

Same as yours. Just a little deep observation of the terms given. :)

Sandeep Bhardwaj - 6 years, 8 months ago

Good solution Megh

Sanjana Nedunchezian - 6 years, 8 months ago

But If we differentiate it and equal it to $0$ we get maxima as $\dfrac{1}{15.3^\dfrac{2}{3}}$

Mehul Chaturvedi - 6 years, 5 months ago

Well n has to be an integer and the practical maxima would be either 6 or 7

Soham Dibyachintan - 5 years, 11 months ago