SELECT * FROM question_mgmt as q WHERE id=1049 AND status=1 SELECT id,question_no,question,chapter FROM question_mgmt as q WHERE courseId=2 AND subId=6 AND chapterId=80 and ex_no='4' AND status=1 ORDER BY CAST(question_no AS UNSIGNED)

Question:

Find the sum to n terms of the series 3 × 12 + 5 × 22 + 7 × 32 + …

Answer:

The given series is 3 ×12 + 5 × 22 + 7 × 32 + …

nth term, an = ( 2n + 1) n2 = 2n3 + n2

therefore space S subscript n space end subscript equals space sum from k equals 1 to n of space a subscript k space space space space space space space space space space space space equals space sum from k equals 1 to n of space open parentheses 2 k cubed space plus space k squared close parentheses space equals space 2 sum from k equals 1 to n of space k cubed space plus space sum from k equals 1 to n of space k squared space space space space space space space space space space space space equals space 2 open square brackets fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction close square brackets squared space plus space fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 6 end fraction space space space space space space space space space space space space equals space fraction numerator n squared open parentheses n plus 1 close parentheses squared over denominator 2 end fraction space plus space fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 6 end fraction space space space space space space space space space space space space space equals fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction open square brackets n open parentheses n plus 1 close parentheses space plus space fraction numerator 2 n plus 1 over denominator 3 end fraction close square brackets space space space space space space space space space space space space space space equals fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction space open square brackets fraction numerator 3 n squared space plus space 3 n space plus space 2 n plus space 1 over denominator 3 end fraction close square brackets space space space space space space space space space space space space space space equals space fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction space open square brackets fraction numerator 3 n squared space plus space 5 n space plus 1 over denominator space 3 end fraction close square brackets space space space space space space space space space space space space space space space equals fraction numerator n open parentheses n plus 1 close parentheses open parentheses 3 n squared space plus space 5 n space plus 1 close parentheses over denominator 6 end fraction

 


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Taking Screenshots on your Samsung Galaxy M31s is very easy and quick.

  • Answered by Ekta Mehta
  • 4 months ago

Taking Screenshots on your Samsung Galaxy M31s is very easy and quick.

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