41/3 + 41/9 + 41/27 + ___________ up to ∞ is equal to
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MATHS
2
1/4
⋅4
1/8
.8
1/16
.16
1/32
.... is equal to
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ANSWER
Converting all bases into bases of 2 we finally need to find sum of AGP
S=
4
1
+
8
2
+
16
3
+⋯
Dividing by 2
2
S
=
8
1
+
16
2
+
32
3
+⋯
Subtracting
2
S
=
4
1
+
8
1
+
16
1
+⋯
Infinite GP
2
S
=
(1−
2
1
)
4
1
S=1 ∴ the value of the expression is 2
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