Ask Uncle Colin: An Enormous Sum | Colin

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can.

Dear Uncle Colin,

I’ve got a question that asks me to find the coefficient of $x^5$ in $(1+x)^5 + (1+x)^6 + (1+x)^7 + … + (1+x)^{100}$.

I can easily work out the coefficient in each term (it’s just $\nCr{k}{5}$), but I can’t see an easy way to add them up. Any ideas?

– Perhaps A Simple Calculation Answers Logically

Hi, PASCAL, and thanks…

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