Question

please help me!!
for the below inequality, what is the greatest possible positive integer value of n?

1/7 + 1/8 -1/9 +1/10 < 1/8 - 1/9 +1/10 + 1/n-3

Answer 1

n=10 gives the equality, any value equal to or larger will violate the inequality.
So the largest positive value of n is 9.

Answer 2

is there any algorythm or anything where i could find out how to do it ? or is it just guess and check ?

Answer 3

Thank you

Answer 4

Well, at least for this particular one, the equality is solved because 1/7 is the missing term on the right. The remaining terms are all identical. So we need 1/7, which is 1/(10-3).
The rest is history.

In general, you would solve for equality and figure which way n can go to maintain the equality.

Answer 5

Great answer many thanks!