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sum of odd numbers from 1 to 99

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 Odd  numbers are 1,3,5,7,9,….,
Odd numbers from 1 to 99=
           1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99.
     by seeing the above there are 50 odd numbers are there from 1 to 99.

Now we will see the sum of elements:
Sum of first 2 odd  numbers: 1+3= 4= 22
Sum of first 3 odd  numbers: 1+3+5= 9= 32
Sum of first 4 odd  numbers: 1+3+5+7=16= 42
Sum of first 5 odd  numbers: 1+3+5+7+9 = 25 = 52
Sum of first n odd  numbers: 1+3+5+7+9+. . . . .  n numbers= n2                               Sum of  odd numbers from 1 to 99: 1+3+5+7+9+. . . . .  50 numbers= 502
                                                                                                                                           
                                                                                                                                            = 50x50
                                                                                                                                            = 2500

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