#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)
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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
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99*(a(1)+a(99))/2
\newcommand{\Bold}[1]{\mathbf{#1}}99 \, c + 4851 \, d
\newcommand{\Bold}[1]{\mathbf{#1}}99 \, c + 4851 \, d
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#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]
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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}
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#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)
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#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]
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sum([d*10^d for d in range(1,8)])
\newcommand{\Bold}[1]{\mathbf{#1}}76543210
\newcommand{\Bold}[1]{\mathbf{#1}}76543210
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#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]
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sum([2^k-k for k in range(1,4)])
\newcommand{\Bold}[1]{\mathbf{#1}}8
\newcommand{\Bold}[1]{\mathbf{#1}}8
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f(n)=2*(2^n-1)-n*(n+1)/2
f(3)
\newcommand{\Bold}[1]{\mathbf{#1}}8
\newcommand{\Bold}[1]{\mathbf{#1}}8
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