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An insect is on point 0 of a number line, hopping towards aim 1. She covers half the s distance from her current location to 1 with each hop. So, she is going to be at $12$ after one hop, $34$ after two hops, and so on. Is it possible for the insect to cross aim 1?

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True

False

answer is B.

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Detailed Solution

It is given that an insect covers half the distance from her current location 0 to 1 with each hop such that she is going to be at

12

after one hop,

34

after two hops, and so on.
The distance covered by the insect is adequate to the current location minus the distance left.
The distance covered within the first hop

= 0 + 12 .

= 12 = 1 − 121

The distance covered within the second hop

= 34 .

= 1 − 14 = 1 − 122

The distance covered within the third hop

= 78 .

= 1 − 18 = 1 − 123

Continuing in the same process, we found that,
The gap covered within the ‘n’ hop

= 1 − 1 2 n .

The insect will never cross 1 because reaching 1,

12 n

must be zero which is not possible for

n ≥ 1.

Thus, it is possible for the insect to cross aim 1.
Hence, option (2) is correct.

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