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 $fraction numerator 1 over denominator 1 cross times 2 end fraction space plus fraction numerator 1 over denominator 2 cross times 3 end fraction space plus space fraction numerator 1 over denominator 3 space cross times space 4 end fraction space plus space...$

Answer:

The given series is $fraction numerator 1 over denominator 1 cross times 2 end fraction space plus space fraction numerator 1 over denominator 2 cross times 3 end fraction space plus fraction numerator 1 over denominator 3 cross times 4 end fraction space plus space...$

nth term, a_n = $fraction numerator 1 over denominator n open parentheses n plus 1 close parentheses end fraction equals 1 over n minus fraction numerator 1 over denominator n plus 1 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis B y space p a r t i a l space f r a c t i o n s right parenthesis$

$a subscript 1 space equals space 1 over 1 space minus space 1 half a subscript 2 space equals space 1 half space minus space 1 third a subscript 3 space space equals space 1 third space minus space 1 fourth... a subscript n space equals space 1 over n space minus space fraction numerator 1 over denominator n plus 1 end fraction$

Adding the above terms column wise, we obtain

$a subscript 1 space plus space a subscript 2 space plus space... space plus space a subscript n space equals space open square brackets 1 over 1 plus 1 half plus 1 third plus...1 over n close square brackets minus open square brackets 1 half plus 1 third plus 1 fourth plus... fraction numerator 1 over denominator n plus 1 end fraction close square brackets therefore space S subscript n space equals space 1 minus space fraction numerator 1 over denominator n plus 1 end fraction equals fraction numerator n plus 1 minus 1 over denominator n plus 1 end fraction equals fraction numerator n over denominator n plus 1 end fraction$

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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 4: Find the sum to n terms of the series ....

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

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