NCERT Solution
Class 11
Mathematics
Sequence and Series
find the sum to nbsp n nbsp terms of the series 3...

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, a_n = ( 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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Question:
Find the sum to n terms of the series 3 × 1² + 5 × 2² + 7 × 3² + …

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