binomial

summation r=1 to r=101 of,

(r)*(101-r)c₅₀

1 Answers

doesn't make sense if 101-r<50

put 101-r=t
so we have summation t=0 to t=100 of
(101-t) ^tC₅₀

=101*^tC₅₀ -t*^tC₅₀

the first one is the 101* the coeff of x⁵⁰ in (1+x)⁵⁰+(1+x)⁵¹...(1+x)¹⁰⁰

the second one is the coeff. of x⁵⁰ in the expansion of the previous expression differentiated once wrt x, and then multiplied by (1+x)

cheers!

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