Q: What is the sum of the first 100 odd numbers using a pattern?

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This is very easy. Simply square the number: 100 squared (100 x 100) = 10,000. So, the sum of the first 100 odd numbers is 10,000.

The sum of the squares of the first 100 natural numbers [1..100] is 338350, while the sum of the first 100 natural numbers squared is 25502500.

There is no known pattern for the distribution of primes.

100

The first five prime numbers between 100 and 200 are: 101 103 107 109 113.

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Do the first say 30 numbers and a pattern should emerge.

The first 100 odd whole numbers are: 13579111315171921232527293133353739414345474951535557596163656769717375777981838587899193959799101103105107109111113115117119121123125127129131133135137139141143145147149151153155157159161163165167169171173175177179181183185187189191193195197199.

The first 100 even numbers are: 2 468101214161820222426283032343638404244464850525456586062646668707274767880828486889092949698100102104106108110112114116118120122124126128130132134136138140142144146148150152154156158160162164166168170172174176178180182184186188190192194196198200.

The first 100 whole, even numbers are: 2468101214161820222426283032343638404244464850525456586062646668707274767880828486889092949698100102104106108110112114116118120122124126128130132134136138140142144146148150152154156158160162164166168170172174176178180182184186188190192194196198200.

The sum of the first 100 positive even numbers can be calculated using the formula for the sum of an arithmetic series: n*(first term + last term)/2. In this case, the first term is 2, the last term is 200, and n is 100. Therefore, the sum is 10,100.

The sum of the first 100 numbers, excluding zero, is 5,001.

The sum of the first 100 odd numbers is 10,000.

102

The sum of the cubes of the first 100 whole numbers is 25,502,500.

The sum of the first 100 positive even numbers is 10,100.

There are no didgits. None! They do not exist! There are ten digits 0, 1, ... 9 which represent the first ten numbers. Beyond that, numbers are represented using the same ten digits but this is done using the idea of place values.

The first numbers of pi is 3.14159265358979323846264338327950288419716939937510 58209749445923078164062862089986280348253421170679