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The value of ∑ r = 16 30 r + 2 ( r - 3 ) is equal to:

Options

  1. A7775
  2. B7785
  3. C7780
  4. D7770

Correct answer

C. 7780

Step-by-step solution

Given value = ∑ r = 16 30 r + 2 ( r - 3 ) = ∑ r = 1 30 r + 2 ( r - 3 ) - ∑ r = 1 15 r + 2 ( r - 3 ) = n n + 1 2 n + 1 6 - n n + 1 2 - 6 n - m m + 1 2 m + 1 6 - m m + 1 2 - 6 m where n = 30 ,   m = 15 = 8810 - 1030 = 7780

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