18. Let \( f(n)=\frac{4 n+\sqrt{4 n^{2}-1}}{\sqrt{2 n+1}+\sqrt{2 n-1}}, n \in N \) then the remainder when \( f(1)+f(2)+f(3)+\ldots+f(60) \) is divided by 9 is

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PeterPJF · Answer 1 · 2024-03-13T19:10:25+0000

saucy6928, hello

What a problem. The remainder when the sum of this sequence is divided by 9 is: 8

And as a side note, if anyone is interested the sum of this sequence is: 665

khadarabad · Answer 2 · 2024-06-24T17:43:22+0000

Rationalizing denominator

Adding all

f(1)+f(2)+f(3)+….+f(60) = 1330/2 = 665

Reminder when 665 is divided by 9 is 8