Permutations and Combinations

Permutations and Combinations

Question

Find the sum of odd integers from 1 to 2001.

Answer

All the odd integers from 1 to 2001 are 1, 3, 5 , 7 , 9,.............. 2001.
Let space space straight S subscript straight n  denote their sum, i.e. straight S subscript straight n space equals space 1 plus 3 plus 5 plus.... plus 2001.
Here,                      a = 1, d = 2, straight t subscript straight n equals 2001
i.e.,              a + (n - 1) d = 2001                       or               1 + (n - 1)2 = 2001
or                   1 + 2n - 2 = 2001                        or                         2n = 2001 + 1 = 2002
or                       straight n equals 2002 over 2 space equals space 1001

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#6 {main}</pre>                                 [∵  space space straight S subscript straight n space equals space straight n over 2 space left parenthesis straight a space plus space straight l right parenthesis]
                            equals 1001 over 2 left parenthesis 2002 right parenthesis space equals space 1001 space cross times space 1001 space equals space 1002001.

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