What expression Is equivalent to 27/125 (3/5)3 (3/4)2 (3/5) 3 5
2 answers:
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(a)
Substitute <em>x</em> = 3 tan(<em>t</em> ) and d<em>x</em> = 3 sec²(<em>t </em>) d<em>t</em> :
(b) The series
converges by comparison to the convergent <em>p</em>-series,
(c) The series
converges absolutely, since
That is, ∑ (-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ converges absolutely because ∑ |(-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ| = ∑ (<em>n</em> ² + 9)/<em>e</em>ⁿ in turn converges by comparison to a geometric series.