perplexus.info :: Just Math : Which is larger?

Which is larger? (Posted on 2008-06-30)

Which is larger, where n is a natural number:

     99ⁿ + 100ⁿ   or   101ⁿ ?

See The Solution Submitted by pcbouhid

Rating: 4.2500 (4 votes)

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Solution

| Comment 3 of 7 |

99ⁿ + 100ⁿ > 101ⁿ where natural number n < 49, and
99ⁿ + 100ⁿ < 101ⁿ where natural number n >= 49

99⁴⁸ + 100⁴⁸ =
1617290140942288185336108527714065
4376666780078410155984946941482067
05262569099287208400715275201

and 101⁴⁸ =
1612226077682464366162063721580560
4379588397845435231244069431329964
71824157105135854515307284801

As can be seen, 99⁴⁸ + 100⁴⁸ > 101⁴⁸

99⁴⁹ + 100⁴⁹ =
1611117239532865303482747442436924
7832900112277626054425097472067246
3820994340829433631670812244899

and 101⁴⁹ =
1628348338459289009823684358796366
0423384281823889583556510125643264
3654239867618721306046035764901

As can be seen, 99⁴⁹ + 100⁴⁹ < 101⁴⁹

Posted by Dej Mar on 2008-06-30 11:23:46

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