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 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …

Answer:

The given series is 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …

nth term, a_n = n ( n + 1)

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

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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:

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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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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 1: Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × ....

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

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