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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 terms is given by (2n – 1)²

Answer:

a_n = (2n – 1)² = 4n² – 4n + 1

$therefore space S subscript n space end subscript equals space sum from k equals 1 to n of space a subscript k space equals space sum from k equals 1 to n of space open parentheses 4 k squared space minus 4 k space plus 1 close parentheses space space space space space space space space space space space equals space 4 sum from k equals 1 to n of space k squared space minus space 4 sum from k equals 1 to n of space k space plus space sum from k equals 1 to n of space 1 space space space space space space space space space space space equals space fraction numerator 4 n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 6 end fraction space minus space fraction numerator 4 n open parentheses n plus 1 close parentheses over denominator 2 end fraction space plus space n space space space space space space space space space space space equals space fraction numerator 2 n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 3 end fraction space minus space 2 n open parentheses n plus 1 close parentheses space plus n space space space space space space space space space space space space equals space n open square brackets fraction numerator 2 open parentheses 2 n squared space plus 3 n space plus 1 close parentheses over denominator 3 end fraction space minus space 2 n open parentheses n plus 1 close parentheses space plus 1 close square brackets space space space space space space space space space space space equals space n open square brackets fraction numerator 4 n squared space plus space 6 n space plus space 2 space minus 6 n space minus 6 space plus 3 over denominator 3 end fraction close square brackets space space space space space space space space space space space space equals space n open square brackets fraction numerator 4 n squared space minus 1 over denominator 3 end fraction close square brackets space space space space space space space space space space space equals space fraction numerator n open parentheses 2 n plus 1 close parentheses open parentheses 2 n minus 1 close parentheses over denominator 3 end fraction$

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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.
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Discuss your answers with your teachers or peers to get feedback and improve your understanding.

Comments

Meghana
2017-09-25 20:02:40

very , very , very ...................................... useful !!!!!!!!!!

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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 10: Find the sum to n terms of the series whose nth terms is given by (2n &ndas....

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

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