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The sum of n terms of 0.7 + 0.77 + 0.777 + … is | StemPy Lab
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The sum of n terms of 0.7 + 0.77 + 0.777 + … is
Mathematics
Hard
High School (11–12)
Algebra › Sequences and Series
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The sum of
n
n
n
terms of
0.7
+
0.77
+
0.777
+
⋯
0.7 + 0.77 + 0.777 + \cdots
0.7
+
0.77
+
0.777
+
⋯
is
7
9
[
n
−
1
9
(
1
−
10
−
n
)
]
\dfrac{7}{9}\left[n - \dfrac{1}{9}\left(1 - 10^{-n}\right)\right]
9
7
[
n
−
9
1
(
1
−
1
0
−
n
)
]
7
9
(
1
−
10
−
n
)
\dfrac{7}{9}\left(1 - 10^{-n}\right)
9
7
(
1
−
1
0
−
n
)
7
9
[
n
+
1
9
(
1
−
10
−
n
)
]
\dfrac{7}{9}\left[n + \dfrac{1}{9}\left(1 - 10^{-n}\right)\right]
9
7
[
n
+
9
1
(
1
−
1
0
−
n
)
]
7
81
(
1
−
10
−
n
)
\dfrac{7}{81}\left(1 - 10^{-n}\right)
81
7
(
1
−
1
0
−
n
)
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← The 2nd term of a geometric progression is 6 and its 5th term is 162. The sum of its first 5 terms is
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