IIT JEE , AIEEE Forum - Mathematics , Algebra - what is the co-efficient of x^98 in (x-1)(x-2)(x-3)..................(x-98)(x-99)(x-100)?"

LastMinuteGenius

for this problem, what you need to do is take the x's from 98 of those product terms (ie. a product term is [x-1] or [x-2],etc) and take the constants from the other 2 terms, so, it is what chirag says:
1*2 + 2*3 + ... + 98*99 + 99*100
general term = r(r+1)
so this is r(r+1)[(r+2) - (r-1)]/3
=> (1/3)*[r(r+1)(r+2) - (r-1)r(r+1)]
summing r from 1 to 99, we get
=> (1/3)*[1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 so on]
as all get cancelled, we get
=> (1/3)*[99.100.101]

so, answer is 33*100*101 => 333,300

RATE if im correct...

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