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Class 11
Mathematics
Sequence and Series
find the sum to nbsp n nbsp terms of the series wh...

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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Question:
Find the sum to n terms of the series whose nth terms is given by (2n – 1)²

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Question: Find the sum to n terms of the series whose nth terms is given by (2n – 1)2

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Question:
Find the sum to n terms of the series whose nth terms is given by (2n – 1)²