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in Mathematics by (71.2k points)

If rth term in the expansion of (axp + b/xq)n is constant, then r =_____

1 Answer

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Best answer

Correct option: 

Explanation:

given: [axp + (b / xq)]n 

Tr+1 = ncr an–r br 

∴ Tr = ncr–1 an–r+1 br–1 

∴ Tr = ncr–1 ∙ (axp)n–r+1 (b / xq)r–1 

∴ rth term is constant

∴ xpn–pr+p ∙ [1 / xqr–q] = 1

i.expn+p+q–pr–qr = x0 

∴ pn + p + q = (p + q)r

∴ r = [(pn + p + q) / (p + q)]

∴ r = 1 + [(pn) / (p + q)]

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