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Statement 1 : The sum of the series 1+(1+2+4)+(4+6+9)+(9+12+16)+ +(361+380+ 400) is 8000 . Statement 2 : _ k=1 ^n (k^3-(k-1)^3 )=n^3 for any natural number n .

Options

  1. AStatement 1 is false, statement 2 is true.
  2. BStatement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
  3. CStatement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
  4. DStatement 1 is true, statement 2 is false

Correct answer

B. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

Step-by-step solution

Statement 1 has 20 terms whose sum is 8000 And statement 2 is true and supporting statement 1 . k^ th bracket is (k-1)^2+k(k-1)+k^2=3 k^2-3 k+1 .

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