Expand ln (1 + sinh x) as a series in ascending powers of x up to and including the term in x^3 . Hence , show that (1 + sinh x)^(3/x) ≅ e^2 (1 −x + (x^2 /2))


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Question Number 83295 by Rio Michael last updated on 29/Feb/20

$Expand \ln (1 + \sinh x) as a series in$ $ascending powers of x up to and including$ $the term in x^{3} . Hence, show that$ ${(1 + \sinh x)}^{\frac{3}{x}} ≅ e^{2} (1 - x + \frac{x^{2}}{2})$
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