1.
(x-1)-\frac{1}{2}(x-1)^{2}+\frac{1}{3}(x-1)^{3}-\frac{1}{4}(x-1)^{4}+\frac{1}{5}(x-1)^{5}+\ldots
2.
\sum _{n=0}^{\infty }(-1)^{n}\frac{x^{2n}}{(2n)!}
3.
1-(x-1)+(x-1)^{2}-(x-1)^{3}+(x-1)^{4}+\ldots
4.
\sum _{n=0}^{\infty }x^{n}
5.
4-4(x-1)+4(x-1)^{2}-4(x-1)^{3}+4(x-1)^{4}+\ldots
6.
(x-1)-\frac{1}{2}(x-1)^{2}+\frac{1}{3}(x-1)^{3}-\frac{1}{4}(x-1)^{4}+\frac{1}{5}(x-1)^{5}+\ldots
7.
\sum _{n=1}^{\infty }(-1)^{n+1}\frac{x^{n}}{n}
8.
1-2(x-1)+3(x-1)^{2}-4(x-1)^{3}+5(x-1)^{4}+\ldots
9.
2-2(x-1)+2(x-1)^{2}-2(x-1)^{3}+2(x-1)^{4}+\ldots
10.
1-x+\frac{1}{2}x^{2}-\frac{1}{6}x^{3}+\frac{1}{24}x^{4}+\ldots
