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\newcommand{\Bold}[1]{\mathbf{#1}}\left[\frac{1}{2}, \frac{1}{6}, \frac{1}{12}, \frac{1}{20}, \frac{1}{30}, \frac{1}{42}\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[\frac{1}{2}, \frac{1}{6}, \frac{1}{12}, \frac{1}{20}, \frac{1}{30}, \frac{1}{42}\right]
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#3)
a(n) = c + n*d
========
a(0) = c
a(1) = c + d
a(2) = c + 2d
a(3) = c + 3d
========
a(0) = c
a(3) = c + 3d
a(6) = c + 6d
a(9) = c + 9d
#4)
a(1) = c + d = 3
a(7) = c + 7d = 21
a(12) = c + 12d = ?
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\newcommand{\Bold}[1]{\mathbf{#1}}\left[4, 12, 36, 108, 324, 972, 2916, 8748, 26244\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[4, 12, 36, 108, 324, 972, 2916, 8748, 26244\right]
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#6)
a(1) = 1 = a*r^(0)
a(11) = 1024 = a*r^(10)
a(21) = (1)*2^(21-1)=2^20=1048576
a(n) = a*r^(n-1)
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\newcommand{\Bold}[1]{\mathbf{#1}}d n + c
\newcommand{\Bold}[1]{\mathbf{#1}}d n + c
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#8)
a(n-1) = a*r^(n-2)
a(n) = a*r^(n-1)
a(n+1) = a*r^(n)
\newcommand{\Bold}[1]{\mathbf{#1}}r^{{\left(n - 1\right)}} {\left| a \right|}
\newcommand{\Bold}[1]{\mathbf{#1}}r^{{\left(n - 1\right)}} {\left| a \right|}
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\newcommand{\Bold}[1]{\mathbf{#1}}\left[0.000000000000000, 0.500000000000000, 0.666666666666667, 0.750000000000000, 0.800000000000000, 0.833333333333333, 0.857142857142857, 0.875000000000000, 0.888888888888889, 0.900000000000000\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[0.000000000000000, 0.500000000000000, 0.666666666666667, 0.750000000000000, 0.800000000000000, 0.833333333333333, 0.857142857142857, 0.875000000000000, 0.888888888888889, 0.900000000000000\right]
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n n/(n+1) 10 0.909090909090909 100 0.990099009900990 1000 0.999000999000999 10000 0.999900009999000 100000 0.999990000099999 n n/(n+1) 10 0.909090909090909 100 0.990099009900990 1000 0.999000999000999 10000 0.999900009999000 100000 0.999990000099999 |
n (n-2)/(n-5) 10 1.60000000000000 100 1.03157894736842 1000 1.00301507537688 10000 1.00030015007504 100000 1.00003000150007 n (n-2)/(n-5) 10 1.60000000000000 100 1.03157894736842 1000 1.00301507537688 10000 1.00030015007504 100000 1.00003000150007 |
n n/sqrt(n^2-1) 10 1.00503781525921 100 1.00005000375031 1000 1.00000050000038 10000 1.00000000500000 100000 1.00000000005000 n n/sqrt(n^2-1) 10 1.00503781525921 100 1.00005000375031 1000 1.00000050000038 10000 1.00000000500000 100000 1.00000000005000 |
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