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Find the sum to n terms of the series whose nth te...

Find the sum to n terms of the | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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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Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

Read the question carefully and focus on the core concept being asked.
Reference examples and data from the chapter when answering questions about Sequence and Series.
Review previous year question papers to get an idea of how such questions may be framed in exams.
Practice answering questions within the time limit to improve your speed and accuracy.
Discuss your answers with your teachers or peers to get feedback and improve your understanding.

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Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 4 , Question 8: Find the sum to n terms of the series whose nth term is given by n (n&....

Find the sum to n terms of the | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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