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

Question:
Find the sum to n terms of the series whose nth term is given by n (n + 1) (n + 4).

Answer:

a_n = n (n + 1) (n + 4) = n(n² + 5n + 4) = n³ + 5n² + 4n

$therefore space S subscript n space equals space sum from k equals 1 to n of space a subscript k space space end subscript space space space space space space space space space space space space equals sum from k equals 1 to n of space open parentheses k cubed space plus space 5 k squared space plus space 4 k close parentheses space space space space space space space space space space space equals space sum from k equals 1 to n of space k cubed space plus space 5 space sum from k equals 1 to n of space k squared space plus space 4 sum from k equals 1 to n of space k 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 open parentheses 2 close parentheses squared end fraction space plus space fraction numerator 5 n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 6 end fraction space plus space fraction numerator 4 n open parentheses n plus 1 close parentheses over denominator 2 end fraction 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 n open parentheses n plus 1 close parentheses over denominator 2 end fraction space plus space fraction numerator 5 open parentheses 2 n plus 1 close parentheses over denominator 3 end fraction space plus space 4 close square brackets 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 3 n space plus space 20 n space plus space 10 space plus 24 over denominator 6 end fraction close square brackets space space space space space space space space space space equals space 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 23 n space plus space 34 over denominator 6 end fraction close square brackets 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 23 n space plus 34 close parentheses over denominator 12 end fraction$

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Question:
Find the sum to n terms of the series whose nth term is given by n (n + 1) (n + 4).

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Question: Find the sum to n terms of the series whose nth term is given by n (n + 1) (n + 4).

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Question:
Find the sum to n terms of the series whose nth term is given by n (n + 1) (n + 4).