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Question: If f(x) = \(\frac { 1 } { 2 ^ { n - 1 } } > \frac { 1 } { 2 ^ { n } } < x \leq \frac { 1 } { 2 ^ { ...

If f(x) = 12n−1>12n<x≤12n−1\frac { 1 } { 2 ^ { n - 1 } } > \frac { 1 } { 2 ^ { n } } < x \leq \frac { 1 } { 2 ^ { n - 1 } } , then the area below the graph of f(x) and above the x-axis between x = 0 and x = 1 is-

A

8/3

B

4/3

C

2/3

D

2

Answer

8/3

Explanation

Solution

Area = = ∑n=0∞122n−1\sum _ { n = 0 } ^ { \infty } \frac { 1 } { 2 ^ { 2 n - 1 } } = 83\frac { 8 } { 3 }