What is the coefficient of x 49 in the product (x-1)(x-3)(x-5) ........... (x-99) ?

Dear Student,   

Please find below the solution to the asked query :

The coefficient of x49 in  the product x-1x-3.....x-99 is given by :coefficient = -1 - 3 - 5 - 7-.........-99 = -1+3+5+7+....+99Let S = 1 + 3 + 5 + .......+99now, above sequence is in AP with a = 1 and d = 2Now, an = 99a+n-1d = 991 + n-12 = 991+2n-2 = 992n = 100n = 50Now, S50 = 5022×1+50-12 = 252+98 = 2500now, S =2500so, required coefficient = -2500
Hope this would clear your doubt !                                                               

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