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Which is larger? (Posted on 2008-06-30) Difficulty: 2 of 5
Which is larger, where n is a natural number:
     99n + 100n   or   101n ?

See The Solution Submitted by pcbouhid    
Rating: 4.0000 (4 votes)

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Basic D2 solution Comment 7 of 7 |

Which is larger depends on what n is. It's clear that for n=1, 99^n + 100^n > 101^n

An easy way to justify that 101^n is larger than 99^n + 100^n once n=100, is to note 99^n + 100^n < 100^n + 100^n. Then, since 1.01^100 = 1+100*.01 + ... then 2<(101/100)^n for n<100, so 2*100^n < 101^n for n=100.

  Posted by Gamer on 2008-06-30 18:35:13
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