If C 0 , C 1 , C 2 , . . . . . , C 20 are the binomial coefficients in the expansion of 1 + x 20 , then the value of C 1 C 0 + 2 C 2 C 1 + 3 C 3 C 2 + . . . . . + 19 C 19 C 18 + 20 C 20 C 19 is equal to (where C r represents C r n )

Question

If C 0 , C 1 , C 2 , . . . . . , C 20 are the binomial coefficients in the expansion of 1 + x 20 , then the value of C 1 C 0 + 2 C 2 C 1 + 3 C 3 C 2 + . . . . . + 19 C 19 C 18 + 20 C 20 C 19 is equal to (where C r represents C r n ), 120, 210, 180, 240

MARKS App · Accepted Answer

C r C r - 1 = n - r + 1 r = 20 - r + 1 r = 21 - r r ⇒ r ⋅ C r C r - 1 = 21 - r ⇒ ∑ r = 1 20 r ⋅ C r C r - 1 = ∑ r = 1 20 21 - r = 21 ∑ r = 1 20 1 - ∑ r = 1 20 r = 21 × 20 - 20 × 21 2 = 210

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