which number is greater ?
99^999 + 1 99^1000 +1
———— OR ———–
99^1000 + 1 99^1001 + 1
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Lets do A – B, ie.
99^999 + 1 99^1000 +1
A – B = ———— – ———–
99^1000 + 1 99^1001 + 1
=> (99^1001 + 1)*(99^999 +1) – (99^1000 + 1 )*(99^1000 +1)
——————————————————–
(99^1000 + 1 ) * (99^1001 + 1)
Now here we just need to see if the value of the numerator is +v or -ve
lets expand the numerator
99^2000 + 99^1001 + 99^999 + 1 – (99^2000 + 99^1000 + 99^1000 + 1)
=> 99^1001 + 99^999 – 2*99^1000
=> 99^999 ( 99^2 + 1 – 2*99)
clearly it is +ve as 99^2 is much greater than 2*99
thus A is greater than B.
