An irrational number \(\sqrt{2}\) and a fraction $$1-\frac{1}{2}$$ and a fact about \(\pi\): $$\frac2\pi = \frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdots$$
show with app
function(input, output, session) {
  output$ex1 <- renderUI({
    withMathJax(helpText('Dynamic output 1:  $$\\alpha^2$$'))
  })
  output$ex2 <- renderUI({
    withMathJax(
      helpText('and output 2 $$3^2+4^2=5^2$$'),
      helpText('and output 3 $$\\sin^2(\\theta)+\\cos^2(\\theta)=1$$')
    )
  })
  output$ex3 <- renderUI({
    withMathJax(
      helpText('The busy Cauchy distribution
               $$\\frac{1}{\\pi\\gamma\\,\\left[1 +
               \\left(\\frac{x-x_0}{\\gamma}\\right)^2\\right]}\\!$$'))
  })
  output$ex4 <- renderUI({
    invalidateLater(5000, session)
    x <- round(rcauchy(1), 3)
    withMathJax(sprintf("If \\(X\\) is a Cauchy random variable, then
                        $$P(X \\leq %.03f ) = %.03f$$", x, pcauchy(x)))
  })
  output$ex5 <- renderUI({
    if (!input$ex5_visible) return()
    withMathJax(
      helpText('You do not see me initially: $$e^{i \\pi} + 1 = 0$$')
    )
  })
}
fluidPage(
  title = 'MathJax Examples',
  withMathJax(),
  helpText('An irrational number \\(\\sqrt{2}\\)
           and a fraction $$1-\\frac{1}{2}$$'),
  helpText('and a fact about \\(\\pi\\):
           $$\\frac2\\pi = \\frac{\\sqrt2}2 \\cdot
           \\frac{\\sqrt{2+\\sqrt2}}2 \\cdot
           \\frac{\\sqrt{2+\\sqrt{2+\\sqrt2}}}2 \\cdots$$'),
  uiOutput('ex1'),
  uiOutput('ex2'),
  uiOutput('ex3'),
  uiOutput('ex4'),
  checkboxInput('ex5_visible', 'Show Example 5', FALSE),
  uiOutput('ex5')
)