Question

How do you use the binomial series to expand `(x+7)^17`?

Answer 1

The binomial theorem states that

where

Hence

where

where `()!` is the factorial function.

Hence we finally get

`(x+7)^17=x^17+119 x^16+6664 x^15+233240 x^14+5714380 x^13+104001716 x^12+1456024024 x^11+16016264264 x^10+140142312310 x^9+980996186170 x^8+5493578642552 x^7+24471395771368 x^6+85649885199788 x^5+230595844768660 x^4+461191689537320 x^3+645668365352248 x^2+564959819683217 x+232630513987207`