Question

Which number is greater - (99^999 + 1)/(99^1000 + 1) OR (99^1000 +1)/(99^1001 + 1)

Note: Answer without calculation...

Answer 1

First number is greater, here is the explanation:

for - (99^999 + 1)/(99^1000 + 1)
consider it as (99^999 + 1)/99^1000 , 99^1000 is big enough that adding 1 does not make a lot of difference
(99^999 + 1)/99^1000= (99^99/99^1000)+(1/99^1000)= (1/99)+1/99^1000 ......(1)

for-(99^1000 +1)/(99^1001 + 1)
consider it as (99^1000 +1)/99^1001
(99^1000 +1)/99^1001=(1/99)+(1/99^1001) ..........(2)

on comparing 1 and 2 we get (99^999 + 1)/(99^1000 + 1) as bigger one.

Answer 2

99 ^ 999 is too big of a number, close to infinite. Adding one 1 to both numerator or denominator does not make any difference, therefore, we can write
99 ^999 / 99 ^ 1000 = 1 / 99 and
99 ^1000 / 99 ^ 1001 = 1 / 99
Then , both numbers are the same

Answer 3

The second number is greater than the first one.

Answer 4

The second number is greater than the first one coz the first number is negative while the second one is positive.

And positive number is always greater than negative number.

Comments

that is not a minus sign