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Byju's Answer
Standard XII
Mathematics
Method of Difference
The value of ...
Question
The value of
0.7
+
0.77
+
0.777
+
…
…
upto
20
terms
is
A
7
81
[
179
−
10
−
20
]
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B
7
9
[
99
−
10
−
20
]
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C
7
81
[
179
+
10
−
20
]
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D
7
9
[
99
+
10
−
20
]
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Solution
The correct option is
C
7
81
[
179
+
10
−
20
]
Let
S
=
0.7
+
0.77
+
0.777
+
…
…
upto
20
terms
⇒
S
=
7
9
[
0.9
+
0.99
+
0.999
+
…
upto
20
terms
]
⇒
9
S
7
=
[
(
1
−
0.1
)
+
(
1
−
0.01
)
+
(
1
−
0.001
)
+
…
upto
20
terms
]
⇒
9
S
7
=
20
−
[
1
10
+
1
100
+
1
1000
+
.
.
.
upto
20
terms
]
⇒
9
S
7
=
20
−
1
10
⎛
⎜ ⎜ ⎜ ⎜ ⎜
⎝
1
−
(
1
10
)
20
1
−
1
10
⎞
⎟ ⎟ ⎟ ⎟ ⎟
⎠
⇒
9
S
7
=
20
−
1
−
10
−
20
9
⇒
S
=
7
81
[
179
+
10
−
20
]
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