find out the largest termof the sequence.1/503,,,4/524,,9/581,,16/692?

Question

this is the sum related to progration...plzzz solve it .....I need it very badly...

Answer 1

The numerators are related by the formula: x^2
The denominators are related by the formula: 3x^3 + 500

Thus, the sequence is:
1 / 503, 4 / 524, 9 / 581, 16 / 692, ... , x^2 / (3x^3 + 500)

Let y = x^2 / (3x^3 + 500)

Now take the derivative and set it equal to zero.

y ' = [(3x^3 + 500)2x - x^2(9x^2)] / (3x^3 + 500)^2 = 0

Multiply through by the denominator:
(3x^3 + 500)2x - x^2(9x^2) = 0

Divide through by x and rearrange:
(we can divide by x because it won't be zero)
(3x^3 + 500)2 = x(9x^2)

Multiply out:
6x^3 + 1000 = 9x^3

3x^3 = 1000

x = 10 / 3^(1/3) = 6.9336

This is closest to the integer 7, so the largest
term should be when x = 7.

This gives the largest term as:
7^2 / (3*7^3 + 500)

= 49 / 1529

Answer 2

R u asking for the nth term ??? cuz this series can go on and on...and it will result only in infinity

Answer 3

Of couse -ve infinity.

Answer 4

INFINITY