**1**+ 3 + 5 + 7 + 9 + ... + 97 + 99 Look at the first and last**numbers**:**1**+ 99 Then the next two: 3 + 97 Then the next two 5 + 95 etc. 49 + 51 They all add up**to 100**and you have 25 pairs. Answer: 2500 Another way ...11 Answers · Science & Mathematics · 05/09/2008

The sum of the squares of the odd

**numbers**from**1 to**99 (**100**isn't included as it is even...i=**1 to**49) i^2 + 4 * sum(i=**1 to**49) i + sum(i=**1 to**49)**1**=**1**+ 4 * 49(49 +**1**)(98 +**1**)/6 + 4 * 49(49...3 Answers · Science & Mathematics · 15/08/2010

From

**1 to 100**you have**100 numbers**. The average ...50-20 = 30 but since both end**numbers**are counted you add**1**. 30+**1**=31.**To**see this count the number...8 Answers · Science & Mathematics · 29/10/2007

...the sum is the product of n and the even number between the two middle

**numbers**. For**1**-**100**, this works out**to**be 50. And for**1**- 1000, it does work out**to**be 418 (http://en.wikipedia...2 Answers · Science & Mathematics · 04/12/2009

The sum of the squares of the even

**numbers**from**1 to 100**is: 2^2 + 4^2 + 6^2 + ... +**100**^2 => sum(i=**1 to**50) (2i)^2 = sum(i=**1**...2 Answers · Science & Mathematics · 15/08/2010

...101 2 + 99 = 101 3 + 98 = 101 ... 49 + 52 = 101 50 + 51 = 101 The sum of all

**numbers**from**1 to 100**, should be the same as adding 101**to**itself 50 times By...8 Answers · Science & Mathematics · 27/12/2017

You pair them off:

**1**+99 =**100**2 + 98 =**100**3 + 97 =**100**... 48+52 =**100**49 + 51 =**100**That's 49...http://en.wikipedia.org/wiki/Arithmetic_series#Sum_.28arithmetic_series.29**1**+ 2 + ... + n = n(n+**1**) / 27 Answers · Science & Mathematics · 01/08/2007

...give it a try. First, write out all the

**numbers**from**1 to 100**. It will be convenient if you lay... is complete for the**numbers 1 to 100**. Every number that is...4 Answers · Science & Mathematics · 03/07/2009

...in his head in under 10 seconds. He reasoned thus:

**1**+**100**= 101 2 + 99 = 101 3 + 98 = 101 There are fifty such pairs, each adding up**to**101. 50 x 101 = 5,050.14 Answers · Science & Mathematics · 16/07/2007

...then there are

**100***101/2 = 5050 dots which is also the sum from**1 to 100**.5 Answers · Science & Mathematics · 31/07/2011