, find the decimal form of 1/5 +1/5²+ 1/5³
Answers
Answered by
2
Answer:
The sum of the series by the binomial theorem, if 0≤x<1, we have,
(1+x)
1
=1−x+x
2
−x
3
+....
Integrating between limits 0 to 1
∫
0
1
(1+x)
dx
=∫
0
1
(1−x+
2
−x
3
+...)
[log(1+x)]
0
1
=[x−
2
x
2
+
3
x
3
−
4
x
4
+....]
0
1
⇒ log(1+1)−log(1−0)=[1−
2
1
+
3
1
−
4
1
+..]−0
⇒ log2=1−
2
1
+
3
1
−
4
1
+....
Attachments:
Answered by
1
Answer:
answer is ०. 248
Explanation:
(0.2)+(0.2)^2 +(0.2)^3
0.2 + 0.04+ 0.008
0.248
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