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Byju's Answer
Standard XII
Mathematics
Differentiation to Solve Modified Sum of Binomial Coefficients
What is the s...
Question
What is the sum of the series
0.5
+
0.55
+
0.555
+
.
.
.
.
to
n
terms?
A
5
9
[
n
−
2
9
(
1
−
1
10
n
)
]
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B
1
9
[
5
−
2
9
(
1
−
1
10
n
)
]
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C
1
9
[
n
−
5
9
(
1
−
1
10
n
)
]
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D
5
9
[
n
−
1
9
(
1
−
1
10
n
)
]
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Solution
The correct option is
D
5
9
[
n
−
1
9
(
1
−
1
10
n
)
]
0.5
+
0.55
+
0.555
+
.
.
.
.
.
.
.
.
.
.
.
.
n
t
e
r
m
s
=
5
{
0.1
+
0.11
+
0.111
+
.
.
.
.
.
.
.
.
}
=
5
9
(
9
10
+
99
100
+
999
1000
+
.
.
.
.
.
.
.
.
.
.
)
=
5
9
(
1
−
1
10
+
1
−
1
100
+
1
−
1
1000
+
.
.
.
.
.
.
.
n
t
e
r
m
s
)
=
5
9
(
n
−
(
1
10
+
1
100
+
1
1000
+
.
.
.
.
.
.
.
.
.
n
t
e
r
m
s
)
)
Now,
1
10
,
1
100
,
1
1000
,.... are in GP
∴
0.5
+
0.55
+
0.555
+
.
.
.
.
.
.
.
.
.
.
.
.
n
t
e
r
m
s
=
5
9
(
n
−
(
1
10
(
1
−
(
1
10
)
n
)
1
−
1
10
)
)
=
5
9
[
n
−
1
9
(
1
−
1
10
n
)
]
Suggest Corrections
0
Similar questions
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Q.
The sum of n terms of the series
1
√
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+
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√
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.
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is
Q.
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