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Algebra 2
Sum of finite series starts from 1
∑
n
=
1
∞
ln
(
n
)
−
ln
(
n
+
1
)
\sum_{n=1}^{\infty}\ln(n)-\ln(n+1)
∑
n
=
1
∞
ln
(
n
)
−
ln
(
n
+
1
)
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∑
k
=
1
∞
(
sin
100
)
k
\sum_{k=1}^{\infty}(\sin 100)^{k}
∑
k
=
1
∞
(
sin
100
)
k
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∑
n
=
1
∞
ln
(
n
2
+
1
2
n
2
+
1
)
\sum_{n=1}^{\infty}\ln\left(\frac{n^{2}+1}{2n^{2}+1}\right)
∑
n
=
1
∞
ln
(
2
n
2
+
1
n
2
+
1
)
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∑
n
=
1
∞
3
n
+
1
4
−
n
\sum_{n=1}^{\infty}3^{n+1}4^{-n}
∑
n
=
1
∞
3
n
+
1
4
−
n
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∑
n
=
1
∞
1
4
+
e
−
n
\sum_{n=1}^{\infty}\frac{1}{4+e^{-n}}
n
=
1
∑
∞
4
+
e
−
n
1
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Simplify to create an equivalent expression.
\newline
−
3
(
2
+
4
k
)
+
7
(
2
k
−
1
)
-3(2+4k)+7(2k-1)
−
3
(
2
+
4
k
)
+
7
(
2
k
−
1
)
\newline
Choose
1
1
1
answer:
\newline
(A)
2
k
−
13
2k-13
2
k
−
13
\newline
(B)
8
k
−
13
8k-13
8
k
−
13
\newline
(C)
2
k
+
13
2k+13
2
k
+
13
\newline
(D)
2
k
−
7
2k-7
2
k
−
7
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Let
f
(
x
)
=
x
2
ln
(
x
)
f(x)=\frac{x^{2}}{\ln (x)}
f
(
x
)
=
l
n
(
x
)
x
2
.
\newline
Find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
2
x
2
2 x^{2}
2
x
2
\newline
(B)
2
x
ln
(
x
)
−
x
(
ln
(
x
)
)
2
\frac{2 x \ln (x)-x}{(\ln (x))^{2}}
(
l
n
(
x
)
)
2
2
x
l
n
(
x
)
−
x
\newline
(C)
2
x
ln
(
x
)
+
x
2 x \ln (x)+x
2
x
ln
(
x
)
+
x
\newline
(D)
2
x
−
1
x
2 x-\frac{1}{x}
2
x
−
x
1
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What is the area of the region between the graphs of
f
(
x
)
=
−
x
2
+
2
x
+
12
f(x)=-x^{2}+2 x+12
f
(
x
)
=
−
x
2
+
2
x
+
12
and
g
(
x
)
=
x
2
−
12
g(x)=x^{2}-12
g
(
x
)
=
x
2
−
12
from
x
=
−
3
x=-3
x
=
−
3
to
x
=
4
x=4
x
=
4
?
\newline
Choose
1
1
1
answer:
\newline
(A)
52
3
13
−
1
−
32
3
\frac{52}{3} \sqrt{13}-1-32 \sqrt{3}
3
52
13
−
1
−
32
3
\newline
(B)
83
3
\frac{83}{3}
3
83
\newline
(C)
7
7
7
\newline
(D)
343
3
\frac{343}{3}
3
343
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Find the sum of the finite series.
\newline
∑
i
=
1
50
(
2
i
−
1
)
(
2
i
+
1
)
\sum_{i=1}^{50} (2i-1)(2i+1)
∑
i
=
1
50
(
2
i
−
1
)
(
2
i
+
1
)
\newline
______
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