which number is greater ?

99^999 + 1 99^1000 +1

———— OR ———–

99^1000 + 1 99^1001 + 1

Check your answer:- Click here to See Solution

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.

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Rajaram Chandra Sah (Raju) says

1st one is greater because the numerator is increasing less than the denominator.