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Find the sum to n terms of the series 12 + (12 + 2...

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 1² + (1² + 2²) + (1² + 2² + 3²) + …

Answer:

The given series is 1² + (1² + 2²) + (1² + 2² + 3³ ) + …

a_n = (1² + 2² + 3³ +…….+ n²)

$equals fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 6 end fraction equals fraction numerator n open parentheses 2 n squared space plus space 3 n space plus 1 close parentheses over denominator 6 end fraction space equals space fraction numerator 2 cubed space plus space 3 n squared space plus space n over denominator 6 end fraction equals space 1 third n cubed space plus space 1 half space n squared space plus space 1 over 6 space n therefore space S subscript n space equals space sum from k equals 1 to n of space a subscript k space space space space space space space space space space equals sum from k equals 1 to n of space open parentheses 1 third space k cubed space plus space 1 half space k squared space plus space 1 over 6 space k close parentheses space space space space space space space space space space equals space 1 third space sum from k equals 1 to n of space k cubed space plus space 1 half space sum from k equals 1 to n of space k squared space plus space 1 over 6 space sum from k equals 1 to n of space k space space space space space space space space space equals 1 third fraction numerator n squared space open parentheses n plus 1 close parentheses squared over denominator open parentheses 2 close parentheses squared end fraction space plus space 1 half space cross times 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 1 over 6 space cross times fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction space space space space space space space space space equals space fraction numerator n open parentheses n plus 1 close parentheses over denominator 6 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 open parentheses 2 n plus 1 close parentheses over denominator 2 end fraction plus 1 half close square brackets space space space space space space space space space equals space fraction numerator n open parentheses n plus 1 close parentheses over denominator 6 end fraction space open square brackets fraction numerator n squared space plus space n space plus space 2 n space plus 1 space plus 1 over denominator 2 end fraction close square brackets space space space space space space space space equals space fraction numerator n open parentheses n plus 1 close parentheses over denominator 6 end fraction space open square brackets fraction numerator n open parentheses n plus 1 close parentheses plus 2 open parentheses n plus 1 close parentheses over denominator 2 end fraction close square brackets space space space space space space space space equals space fraction numerator n open parentheses n plus 1 close parentheses over denominator 6 end fraction space open square brackets fraction numerator open parentheses n plus 1 close parentheses open parentheses n plus 2 close parentheses over denominator 2 end fraction close square brackets space space space space space space space space equals space fraction numerator n open parentheses n plus 1 close parentheses squared open parentheses n plus 2 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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2018-09-17 19:26:41

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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 7: Find the sum to n terms of the series 12 + (12 + 22) + (12 + 22 + 32) ....

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

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