Question 127(iii)

An insect is on the 0 point of a number line, hopping towards 1. She covers half the distance from her current location to 1 with each hop.
So, she will be at $\frac{1}{2}$ after one hop, $\frac{3}{4}$ after two hops and so on.

Will the insect ever get to 1? Explain.

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Solution

No, because for reaching 1, ${(\frac{1}{2})}^{n}$ has to be zero for some finite n which is not possible.

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Question 127(i)

An insect is on the 0 point of a number line, hopping towards 1. It covers half the distance from its current location to 1 with each hop.
So, it will be at $\frac{1}{2}$ after one hop, $\frac{3}{4}$ after two hops and so on.

Make a table showing the insects location for the first 10 hops.

Question 127(ii)

Question 127(i)

Q. A bunny hops on a number line. He is standing at number 6. He hops steps backward to reach number 3.

Q. Finny hops to number 8 first and then moves 9 steps forward. Where is she on the number line?

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Question 127(iii) An insect is on the 0 point of a number line, hopping towards 1. She covers half the distance from her current location to 1 with each hop. So, she will be at 12 after one hop, 34 after two hops and so on. Will the insect ever get to 1? Explain.

No, because for reaching 1, (12)n has to be zero for some finite n which is not possible.

Question 127(iii)

An insect is on the 0 point of a number line, hopping towards 1. She covers half the distance from her current location to 1 with each hop.
So, she will be at $\frac{1}{2}$ after one hop, $\frac{3}{4}$ after two hops and so on.

Will the insect ever get to 1? Explain.

No, because for reaching 1, ${(\frac{1}{2})}^{n}$ has to be zero for some finite n which is not possible.