Find the exact value of a sequence
- Thread starter thatguy47
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I'm not saying your answer is wrong, but you forgot about the sum for sin.
\(\displaystyle S_n \le \frac{3}{n}\sum_{k=1}^{n}(1) = 3\)
The fact that it converges is due to sin(1+3k/n) always being positive except for when 1+3k/n > pi, but regardless as n gets bigger, for the values in the first quadrant alone, you can see that the sum is increasing and bounded above by 3.
\(\displaystyle S_n \le \frac{3}{n}\sum_{k=1}^{n}(1) = 3\)
The fact that it converges is due to sin(1+3k/n) always being positive except for when 1+3k/n > pi, but regardless as n gets bigger, for the values in the first quadrant alone, you can see that the sum is increasing and bounded above by 3.
BigGlenntheHeavy
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\(\displaystyle -1 \ \le \ sin(anything) \ \le \ 1\)
\(\displaystyle Does \ that \ tell \ you \ anything?\)
\(\displaystyle Does \ that \ tell \ you \ anything?\)