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the coefficirent of x^99 in (x+1) (x+3) (x+5) ......(x+199) is????? PLS EXPLAIN!!

the coefficirent of x^99 in (x+1) (x+3) (x+5) ......(x+199) is?????


PLS EXPLAIN!!

Grade:9

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Shivam,

 

If you note there are 100 terms in the bracket, in the product in the above Question.

So if you consider any 99 brackets, you will have co-eff of x^99 as 1..... and the other one bracket will be left. So the constant term in the left over bracket will be the co-eff of x^99 in that case.

Remember you can choose any of the 99 brackets - and one left over bracket.

 

So co-eff of x^99 in the above product will be:

1+3+5+.....+199 = 100/2 * (1+199) = 100*100 = 10000.

 

Hope it helps.

 

Wish you all the best.

 

Regards,

Ashwin (IIT Madras).

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