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Find the coefficient of x5 in the expansion of (1 + x) 21 { 1+ ( 1 + x) … + (1 − x)}9

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Given, (1+x) 21 {1 + (1 + ) +. . . (1 − ) 9 }

  = (1+x) 21 \(\frac{1+x^{10}-1}{1+x-1}\)

\(\frac{1}{x}\)[(1 +x) 31 − (1 + x) 21]

∴ Coefficient of x5 in this expression = coefficient of x6 in the expansion[(1 +x) 31 − (1 + x) 21]

= 31C6 21C6

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