10th term (g-4)^15

 
 
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The binomial expansion is related to Pascal's triangle in which every row is related to the previous row by simple addition of terms. In the expansion of the binomial (a+b)^n the coefficients of consecutive terms are n, n(n-1)/2, n(n-1)(n-2)/6, ... n(n-1)(n-2)...(n-r+1)/1*2*...*r, where r is the general term. If n=15 and r=10, the coefficient is 3003. This is also the value of the combination function nCr and is the 10th term in the 15th row of Pascal's triangle. The variables a and b for the 10th term are a^r*b^(n-r). a=g and b=-4, so the 10th term is 3003g^10*(-4)^5=-3075072g^10. There is an ambiguity in stating the rth term, depending on whether r starts from 0 or 1. The coefficient for r=9 is 5005 and the other components will also be affected.

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9Tr+1 =    n^c^r (1st^ r) (2nd ^(n-r)     t9+1 =  15^c^9 (9^9)(-4)^(15-9)  =1586874328000


 

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