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Byju's Answer
Standard XII
Mathematics
Substitution Method to Remove Indeterminate Form
limx→∞1+12+14...
Question
lim
x
→
∞
1
+
1
2
+
1
4
+
.
.
.
.
+
1
2
n
1
+
1
3
+
1
9
+
.
.
.
.
+
1
3
n
=
A
4
3
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B
3
4
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C
1
2
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D
0
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Solution
The correct option is
A
4
3
Use G.P formula of summation
∞
Σ
p
=
l
=
1
1
−
x
Therefore,
1
1
−
1
2
1
1
−
1
3
=
2
3
2
=
4
3
Hence, option 'A' is correct.
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0
Similar questions
Q.
lim
n
→
∞
1
+
1
2
+
1
4
+
.
.
.
+
1
2
n
1
+
1
3
+
1
9
+
.
.
.
+
1
3
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Q.
Solve
lim
n
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1
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⋯
+
1
2
n
1
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3
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Q.
2
C
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+
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C
1
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C
2
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2
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C
3
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+
.
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.
.
.
.
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+
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n
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+
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−
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+
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Q.
Find the value of n such that
2
3
(
4
n
−
1
)
−
(
2
n
−
1
+
n
3
)
=
1
3
n
+
4
3
.
Q.
If
n
∑
r
=
1
T
r
=
(
3
n
−
1
)
,
then the value of
n
∑
r
=
1
1
T
r
is
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