A portion of a triangular array of numbers is given below

MATHEMATICS · Multi-part · CBSE · Mathematics · Binomial Theorem · Binomial Theorem

Problem

A portion of a triangular array of numbers is given below. The symbols p,  q,  r,  sp,\;q,\;r,\;s stand for missing positive integers. Row 0 : \;1 Row 1 : \;1\;\;1 Row 2 : \;1\;\;2\;\;1 Row 3 : \;1\;\;p\;\;3\;\;1 Row 4 : \;1\;\;4\;\;q\;\;4\;\;1 Row 5 : \;1\;\;5\;\;10\;\;r\;\;5\;\;1 Row 6 : \;1\;\;6\;\;15\;\;20\;\;s\;\;6\;\;1 (i) Determine the values of p,  q,  rp,\;q,\;r and ss. (ii) Using the complete set of numbers in Row 5, expand (x+2)5(x+2)^{5}.

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