If you take a watch at sum of first n weird numbers, friend can notice very interesting pattern.

You are watching: Sum of 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, amount of an initial n odd number is equal to

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. Similarly, sum of first 25 odd numbers would be same to

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.

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

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

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i beg your pardon is equal to amount of an initial 50 weird numbers.

 

Application:

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

 

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

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. Right here n = 100 since we recognize that there are 100 odd numbers from 1 and 200. (1 + 3 + 5 + 7 + 9 + …. 199 ) is the sum of very first 100 strange numbers.

 

We additionally 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, amount of an initial n odd numbers


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