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a k = sin ( 2 π k 4 + 4 k ) {\displaystyle a_{k}=\sin {\Bigg (}{\frac {2\pi k}{4+4k}}{\Bigg )}}
1 2 {\displaystyle {\frac {1}{\sqrt {2}}}}
∑ k = 2 ∞ 4 k − 2 5 k − 1 {\displaystyle \sum _{k=2}^{\infty }{\frac {4^{k-2}}{5^{k-1}}}}
∑ k = 1 ∞ ( 1 k + 4 − 1 k + 5 ) {\displaystyle \sum _{k=1}^{\infty }{\Bigg (}{\frac {1}{k+4}}-{\frac {1}{k+5}}{\Bigg )}}
a n = { 2 − 1 n if n is odd 1 + 1 n if n is even {\displaystyle a_{n}={\begin{cases}2-{\frac {1}{n}}&{\text{if }}n{\text{ is odd}}\\1+{\frac {1}{n}}&{\text{if }}n{\text{ is even}}\end{cases}}}
1 1 + 1 3 + 1 5 + 1 7 + … {\displaystyle {\frac {1}{1}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{7}}+\ldots }
∑ k = 1 ∞ ( x − 1 ) k ( k + 2 ) 2 k ( k + 3 ) {\displaystyle \sum _{k=1}^{\infty }{\frac {(x-1)^{k}(k+2)}{2^{k}(k+3)}}}
∑ k = 1 ∞ ln ( k 2 + 3 k 2 + 2 k + 4 ) {\displaystyle \sum _{k=1}^{\infty }\ln {\Bigg (}{\frac {k^{2}+3}{k^{2}+2k+4}}{\Bigg )}}
∑ k = 1 ∞ k k ( 3 k ) ! {\displaystyle \sum _{k=1}^{\infty }{\frac {k^{k}}{(3k)!}}}
∑ k = 1 ∞ ( − 1 ) k k − p {\displaystyle \sum _{k=1}^{\infty }{\frac {(-1)^{k}}{k-p}}}
f ( x ) = 4 16 x 2 − 1 {\displaystyle f(x)={\frac {4}{16x^{2}-1}}}
f ( x ) = e 5 x cos ( 5 x ) {\displaystyle f(x)=e^{5x}\cos(5x)}
Equation 1
∫ e − x 2 d x {\displaystyle \int e^{-x^{2}}dx}
Equation 2
D + x + x 3 a + … {\displaystyle D+x+{\frac {x^{3}}{a}}+\ldots }
f ( x ) = sin ( 2 x ) 3 x {\displaystyle f(x)={\frac {\sin(2x)}{3x}}}
∑ k = 0 ∞ x 8 k k ! {\displaystyle \sum _{k=0}^{\infty }{\frac {x^{8k}}{k!}}}
