The general term of the binomial (a+b)^n?

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Answer 1 · 2017-05-01T21:10:45

See explanation

It all depends on the value of n. If you reference Pascal's triangle you can observe just how much this changes>

Tony B

Suppose n=6 then you would look at the line #x^6#

But first lets build the all the indices (powers)

By the way; #b^0=1# as does #a^0=1#

#a^6b^0+a^5b^1+a^4b^2+a^3b^3+a^2b^4+a^1b^5+a^0b^6#

Now we add in the coefficients from line 6

#1"; "6"; "15"; "20"; "15"; "6"; "1#

#a^6+6a^5b^1+15a^4b^2+20a^3b^3+15a^2b^4+6a^1b^5+b^6#

If I remember correctly; In general terms we have:

#sum_(i=0ton) color(white)()^nC_i color(white)(.)a^(n-i)b^i#

Lets test for #15a^4b^2->" where "i=2#

#(n!)/((n-i)!i!) -> (6!)/(4!2!) = (6xx5xxcancel(4!))/(cancel(4!)xx2xx1)#

#" "=3xx5=15#