9no see itll be diffrentiation of t(1-t1001)/1-t
find the coefficient of x50 in the expression
(1+x)1000+2x(1+x)999+3x2(1+x)998+...+1000x999(1+x)+1001x1000
may be it is a sum from any common book bu i do not have the solution .i found it in my state book exercise.
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3 Answers
9gvn
= (1+x)1000.(1+2t+3t2................1001t1000)
=(1+x)1000. f(t)
where t =x/1+x
f(t) = d/dt ( ∫ f(t) dt )
now proceed
i must accept this is quite a long sum
another way is
Σ r.C1001-r51-r
but simplifying this is not very easy
1couldn"t understand integrating it and then deriving it will bring me to the same step