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Cara Duke

Cara Duke

Answered question

2022-05-22

Consider n N , n > 1. The sum S = 1.1 2 + 3.2 2 + 5.3 2 + 7.4 2 + + ( 2 n 1 ) n 2 converges to what value in terms of n?

Answer & Explanation

Makai Blackwell

Makai Blackwell

Beginner2022-05-23Added 11 answers

There is a whole lot of difference between "convergence" and a formula.
n n 2 ( 2 n 1 ) = n ( 2 n 3 n 2 ) = 2 n n 3 n n 2 = 2 ( n ( n + 1 ) 2 ) 2 n ( n + 1 ) ( 2 n + 1 ) 6
Simplify the above yo get your required form.
You can use a proof by induction to prove that n n 3 = ( n ( n + 1 ) 2 ) 2 and n n 2 = n ( n + 1 ) ( 2 n + 1 ) 6

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