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the sum of the series 11 2 12 3 13 4
Question:
The sum of the series
1
1.2
−
1
2.3
+
1
3.4
−
…
.
.
∞
WBJEE
Updated On:
Aug 1, 2023
(A) 2loge 2 + 1
(B) 2loge 2
(C) 2loge 2 – 1
(D) loge 2 – 1
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The Correct Option is
C
Solution and Explanation
Explanation:
s
=
1
1.2
−
1
2.3
+
1
3.4
…
…
∞
=
(
1
1
−
1
2
)
−
(
1
2
−
1
3
)
+
(
1
3
−
1
4
)
=
1
1
−
1
2
−
1
2
+
1
3
+
1
3
−
1
4
−
1
4
+
1
5
…
=
1
1
−
2
2
+
2
3
−
2
4
+
2
5
−
…
=
2
[
1
1
−
1
2
+
1
3
−
1
4
+
1
5
…
]
−
1
=
2
log
2
−
1
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