Binomial

[IloveManUtd]

If the coefficients of x[sup:2dv5pkzn]k[/sup:2dv5pkzn] and x[sup:2dv5pkzn]k+1[/sup:2dv5pkzn] in the expansion of (2+3x)[sup:2dv5pkzn]19[/sup:2dv5pkzn] are equal, find k

I've got the answer through the tables book but am wondering if there is a way to calculate it manually. PLEASE help.

 

[Deleted member 4993]

If the coefficients of x[sup:707bx01n]k[/sup:707bx01n] and x[sup:707bx01n]k+1[/sup:707bx01n] in the expansion of (2+3x)[sup:707bx01n]19[/sup:707bx01n] are equal, find k

I've got the answer through the tables book but am wondering if there is a way to calculate it manually. PLEASE help.

Look up in your textbook about general coefficients of x[sup:707bx01n]k[/sup:707bx01n] in the expansion of (ax + b)[sup:707bx01n]n[/sup:707bx01n]. It will be something like(may not be exactly equal to) [sub:707bx01n]n[/sub:707bx01n]C[sub:707bx01n]n-k[/sub:707bx01n] * a[sup:707bx01n]k[/sup:707bx01n]*b[sup:707bx01n]n-k[/sup:707bx01n] and continue from there....