
A particle begins at the origin and moves successively in the following manner as shown. unit to the right. unit up. Unit to the right. unit down. to the right etc. the length of each move is half. The length of the previous move and movement continues in a zigzag manner indefinitely. The coordinate of the point to which the zigzag converges is

Answer
426.3k+ views
Hint: If the number of the terms in the GP is finite then the GP is called the infinite GP.
To calculate the common ratio, divide the second term of the sequence with the first term.
The infinite GP doesn’t have the last term. In this infinite GP when the common ratio is greater than 1 then the series will be larger
Complete answer:
Along x-direction, the distance is the sum of ... (common ratio= )..so on by adding this infinite GP, we get
Similarly, along y, the movement is as ..... so this GP of common ratio (- ) adds up to
In other ways,
Consider x-axis
It is an infinite GP with and
Hence it becomes,
From this the x coordinate is
By Considering the y axis
-…
Now It is an infinite GP with and
Now the equation becomes,
So, y coordinate
The zigzag converging point is
Hence option (B) is the answer.
Note: Finally, The zigzag converging point is
The G.P is the geometric progression that contains the non-zero numbers.
Infinite geometric series is calculated by the sum of the infinite geometric sequence.
To calculate the common ratio, divide the second term of the sequence with the first term.
The infinite GP doesn’t have the last term. In this infinite GP when the common ratio is greater than 1 then the series will be larger
Complete answer:
Along x-direction, the distance is the sum of
Similarly, along y, the movement is as
In other ways,
Consider x-axis
It is an infinite GP with
Hence it becomes,
From this the x coordinate is
By Considering the y axis
Now It is an infinite GP with
Now the equation becomes,
So, y coordinate
The zigzag converging point is
Hence option (B) is the answer.
Note: Finally, The zigzag converging point is
The G.P is the geometric progression that contains the non-zero numbers.
Infinite geometric series is calculated by the sum of the infinite geometric sequence.
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