Question

Substitute n=1, 2, 3, 4, 5 and write the first five terms of the sequence \left\{\frac{(-1)^{n-1}x^{2n-1}}{(2n-1)!}\right\}

Sequences
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asked 2021-05-28
Substitute n=1, 2, 3, 4, 5 and write the first five terms of the sequence
\(\left\{\frac{(-1)^{n-1}x^{2n-1}}{(2n-1)!}\right\}\)

Answers (1)

2021-05-29
\(\left\{\frac{(-1)^{n-1}x^{2n-1}}{(2n-1)!}\right\}\)
\(\left\{\frac{(-1)^{1-1}x^{2(1)-1}}{(2(1)-1)!}\right\}=\frac{(-1)^{0}x^{1}}{(1)!}=x\)
\(\left\{\frac{(-1)^{2-1}x^{2(2)-1}}{(2(2)-1)!}\right\}=\frac{(-1)^{1}x^{3}}{(3)!}=-\frac{x^{3}}{6}\)
\(\left\{\frac{(-1)^{3-1}x^{2(3)-1}}{(2(3)-1)!}\right\}=\frac{(-1)^{2}x^{5}}{(5)!}=\frac{x^{5}}{120}\)
\(\left\{\frac{(-1)^{4-1}x^{2(4)-1}}{(2(4)-1)!}\right\}=\frac{(-1)^{3}x^{7}}{(7)!}=-\frac{x^{7}}{5040}\)
\(\left\{\frac{(-1)^{5-1}x^{2(5)-1}}{(2(5)-1)!}\right\}=\frac{(-1)^{4}x^{9}}{(9)!}=\frac{x^{9}}{362880}\)
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