Write down in terms of x and n, the term containing x to the power of 3 in the expansion - Maths - Binomial Theorem

Question

Write down in terms of x and n, the term containing x to the power
of 3 in the expansion of ( 1 - x / n) to the power of n by the
binomial theorem If this term equals 7/8 when x = - 2, and n is a
positive integer, Calculate the value of n?

Anuradha Sharma · Accepted Answer

The general term in x+an is given as, Tr+1=nCrxn-rarSo for 1-xnn, the general term can be given as, Tr+1=nCr1n-r-xnrSo for coefficient of x3 putting r = 3 we getT4=nC31n-3-xn3=-nC3×1n3x3So term containing x3 is, =-nC3×1n3x3Now it is given that at x = -2 it is 78 so-nC3×1n3×-23=78nn-1n-26×8n3=7864n-1n-2=4232n2+64-96n=2132n2-96n+43=0n=96±962-4×32×4364n=2
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Write down in terms of x and n, the term containing x to the power of 3 in the expansion of ( 1 - x / n) to the power of n by the binomial theorem. If this term equals 7/8 when x = - 2, and n is a positive integer, Calculate the value of n?