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 n² + 2n

Answer:

a_n = n² + 2n

$therefore space S subscript n space equals space sum from k equals 1 to n of space k squared space plus space 2 to the power of k space equals space sum from k equals 1 to n of space k squared space space plus space sum from k equals 1 to n of space 2 to the power of k space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis C o n s i d e r space sum from k equals 1 to n of space 2 to the power of k space equals space 2 to the power of 1 space plus space 2 squared space plus 2 cubed space plus space...$

The above series 2, 2², 2³, … is a G.P. with both the first term and common ratio equal to 2.

$therefore space sum from k equals 1 to n of space 2 to the power of k space equals space fraction numerator open parentheses 2 close parentheses open square brackets open parentheses 2 close parentheses to the power of n space minus 1 close square brackets over denominator 2 minus 1 end fraction equals 2 open parentheses 2 to the power of n space minus 1 close parentheses space space space space space space space space space space space... left parenthesis 2 right parenthesis$

Therefore, from (1) and (2), we obtain

$S subscript n space equals space sum from k equals 1 to n of space k squared space plus space 2 open parentheses 2 to the power of n space minus 1 close parentheses space equals space fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 6 end fraction plus 2 open parentheses 2 to the power of n space end exponent minus 1 close parentheses$

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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 9: Find the sum to n terms of the series whose nth terms is given by n2 +....

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

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