For positive integers n, if 4a_n=(n^2+5n+6) and S_n= _k=1^n 0.05em ( 1a_k ), then the value of 507S_2025 is:

Question

Accepted Answer

Correct answer: B. (b) S_n= _k=1^n 0.05em 4K^2+5k+6 = 0.05em 4 (K+2 ) (K+3 )=4 0.05em( 1K+2- 1K+3) =4( 13- 14) =4( 14- 15) =4( 1n+2- 1n+3) S_n=4( 13- 1n+3) S_2025=4( 13- 12028) S_2025=4 ( 6752028 ) 507S_2025=675

$For positive integers n, if 4 a_{n} = (n^{2} + 5 n + 6) and S_{n} = \sum_{k = 1}^{n} (\frac{1}{a _{k}}), then the value of 507 S_{2025} is:$

Solution

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