If you take a watch at amount of first n odd numbers, girlfriend can an alert very exciting pattern.

You are watching: What is the sum of the first 100 odd numbers

1 = 1

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1 + 3 = 4

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1 + 3 + 5 = 9

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1 + 3 + 5 + 7 = 16


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1 + 3 + 5 + 7 + 9 = 25

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1 + 3 + 5 + 7 + 9 + 11 = 36

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So, sum of very first n odd number is same to

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. Similarly, sum of an initial 25 weird numbers would certainly be same to

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.

Using the same concept, can we find sum that (1 + 3 + 5 + 7 + 9 + 11 + ……99).

We know that we have actually 50 odd number from 1 come 100. Therefore, (1 + 3 + 5 + 7 + 9 + 11 + ……99)

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which is equal to sum of very first 50 strange numbers.

 

Application:

Can you discover the value of 101+103+105+107+……199 making use of the same concept? that becomes small tricky here.

 

We know that 1 + 3 + 5 + 7 + 9 + …. 199

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. Below n = 100 due to the fact that we know that there space 100 odd numbers from 1 and 200. (1 + 3 + 5 + 7 + 9 + …. 199 ) is the sum of first 100 strange numbers.

 

We also know that 1 + 3 + 5 + 7 + 9 + …. 99

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(101+103+105+107+……199) = (1 + 3 + 5 + 7 + 9 + ….199) – (1 + 3 + 5 + 7 + …..99) = 10000 – 2500 = 7500

 


Filed Under: Algebra Tagged With: algebra, weird numbers, sum of an initial n weird numbers


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