st
6100
8
Substract the sum - 3
10
from the sum of 4 e 2
5
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1
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MATHS
The sum of
1.2
1
−
2.3
1
+
3.4
1
−
4.5
1
+..... is
December 30, 2019avatar
Mithlesh Bindal
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VIDEO EXPLANATION
ANSWER
As we know that, log(1+x)=x−
2
x
2
+
3
x
3
−
4
x
4
+...
Put x=1
log2=1−
2
1
+
3
1
−
4
1
+...=∑
n=1
∞
n
(−1)
n+1
=1+∑
n=1
∞
n+1
(−1)
n
...(1)
S
∞
=
1.2
1
−
2.3
1
+
3.4
1
−
4.5
1
+.....
⇒S
∞
=∑
n=1
∞
n(n+1)
(−1)
n+1
=∑
n=1
∞
(−1)
n+1
(
n
1
−
n+1
1
)
⇒S
∞
=∑
n=1
∞
n
(−1)
n+1
+∑
n=1
∞
n+1
(−1)
n
⇒S
∞
=log2+log2−1=log2
2
−loge ...[ From (1) ]
⇒S
∞
=log
e
4
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