A number theory problem by Mohammad Arman Khaled
Number Theory
Level
2
~~~~Find the sum of Odd integers from 1 to 300001
The answer is 22500300001.
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Firstly there are (300,001 + 1)/2 odd numbers to account for, which totals up to 150,001.
S = 1 + 3 + 5 + ... + 299,999 + 300,001
Also, S = 300,001 + 299,999 + ... + 5 + 3 + 1
Adding them together gives
2S = 300,002 + 300,002 + ... + 300,002 + 300,002
So S = 150,001 * 150,001, which is half of the term above * the total odd numbers.
Therefore S = 22,500,300,001
The answer on a standard scientific calculator appears to not have a 1 on the end due to not enough characters being display on screen. However this method shows that there should be a 1 on the end due to the units multiplication here.