CM 4.3 Series MrG 2011.1107

3673 days ago by calcpage123

#1) var('c,d') a(n)=c+(n-1)*d show(a(1)) show(a(2)) show(a(3)) show(3*(a(1)+a(3))/2) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}c
\newcommand{\Bold}[1]{\mathbf{#1}}c + d
\newcommand{\Bold}[1]{\mathbf{#1}}c + 2 \, d
\newcommand{\Bold}[1]{\mathbf{#1}}3 \, c + 3 \, d
\newcommand{\Bold}[1]{\mathbf{#1}}c
\newcommand{\Bold}[1]{\mathbf{#1}}c + d
\newcommand{\Bold}[1]{\mathbf{#1}}c + 2 \, d
\newcommand{\Bold}[1]{\mathbf{#1}}3 \, c + 3 \, d
sum([a(n) for n in range(1,100)]) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}99 \, c + 4851 \, d
\newcommand{\Bold}[1]{\mathbf{#1}}99 \, c + 4851 \, d
99*(a(1)+a(99))/2 
       
\newcommand{\Bold}[1]{\mathbf{#1}}99 \, c + 4851 \, d
\newcommand{\Bold}[1]{\mathbf{#1}}99 \, c + 4851 \, d
#3)1/(1*2)+1/(2*3)+1/(3*4)+...+1/(n*(n+1)) #3)1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)=1-1/(n+1) [1/(n*(n+1)) for n in range(1,4)] 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[\frac{1}{2}, \frac{1}{6}, \frac{1}{12}\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[\frac{1}{2}, \frac{1}{6}, \frac{1}{12}\right]
sum([1/(n*(n+1)) for n in range(1,4)]) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{3}{4}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{3}{4}
#4) plot((1-1/2^x,1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024),xmin=0,xmax=10) 
       
#6) [d*10^d for d in range(1,8)] 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[10, 200, 3000, 40000, 500000\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[10, 200, 3000, 40000, 500000\right]
sum([d*10^d for d in range(1,8)]) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}76543210
\newcommand{\Bold}[1]{\mathbf{#1}}76543210
#7)2(2^n-1)-n(n+1)/2 [2^k-k for k in range(1,4)] 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[1, 2, 5\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[1, 2, 5\right]
sum([2^k-k for k in range(1,4)]) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}8
\newcommand{\Bold}[1]{\mathbf{#1}}8
f(n)=2*(2^n-1)-n*(n+1)/2 f(3) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}8
\newcommand{\Bold}[1]{\mathbf{#1}}8