hello, this is the problem:
show that
infinite
Σ sin (1/n^2) is a positive, convergent series.
n=1
Hint: use the inequality sinx is less than or equal to x for x is greater than or equal to 0
Not exactly. First show that 1/n^2 is a converging series. Then use the hint the problem gave, that for n>0, $\displaystyle \sin(n) \le n$. Put another way, $\displaystyle \frac{1}{\sin^2(n)} \le \frac{1}{n^2}$ So we have established a bounding series that converges and this proves that the other series converges as well.