There is a rope and a bamboo pole. When the rope is folded in half, it is 2 meters longer than the bamboo pole. When the rope is folded in four, it is 2 meters shorter than the bamboo pole. How long are the bamboo pole and the rope?

Rope: (2 + 2) △ 12-14, = 4 △ 14, = 16 (m); bamboo pole: 16 × 12-2, = 8-2, = 6 (m); answer: rope is 16 m long, bamboo pole is 6 m long

A rope is 2 meters longer after 2 folds than after 3 folds. How long is this rope?

How can I calculate 16 meters without doing math for a long time
If you fold it twice, it will be 4 segments; if you fold it three times, it will be 8 segments,
Let X be the segment that is folded twice and y be the segment that is folded three times
Then X-Y = 2
4x=8y
Because it's the same rope
The solution is x = 4, y = 2
So the rope is 16 meters

One rope is 8 meters long. First fold it in half and then fold it in half. How many parts of this rope is each rope? How many meters is each rope?

Fold in half once, each section = 8 / 2 = 4m
Fold twice, each section = 4 / 2 = 2m
2 / 8 = 1 / 4, each section is 1 / 4 of the rope
Each section is 2 meters long

A rope is 6 meters long. Fold it in half and then fold it in half. How long is each fold?

6 △ 4 = 32 (m), answer: each fold is 32 m long

Seven bamboo poles are arranged in a row. The first one is 1 meter long, and the other one is half the length of the former one. Q: how long are the seven bamboo poles?

1 + 1 × (12) 1 + 1 × (12) 2 + 1 × (12) 3 + 1 × (12) 4 + 1 × (12) 5 + 1 × (12) 6, = 1 + 12 + 14 + 18 + 116 + 132 + 164, = 1 + 3264 + 1664 + 864 + 464 + 264 + 164, = 1 + 6364, = 16364 (m)

There are 10 bamboo poles in a row. The first one is 1 meter long, and the length of the other one is half of that of the former one

Equal ratio sequence
1 + 1/2 + 1/4 + ...+ 1/(2^9)
= 2 - 1/(2^9) = 2 - 1/512
About 1.998 meters

There are 10 bamboo poles in a row. The first one is 1 meter long, and the other one is half the length of the former one?

Analysis: the degree of the 10 bamboo poles is: 1, 1 / 2, 1 / 4, 1 / 8, 1 / 16
This sequence belongs to the equal ratio sequence: the first term A1 = 1
Common ratio q = 1 / 2
Number of items: n = 10
The first n terms and Sn = A1 (1-Q ^ n) / 1-Q
1+1/2+1/4+.+1/512
=1×[1-（1/2）^n] ÷ (1-1/2)
=2-(1/2）^ 9

There are four bamboo poles in a row. The first one is one meter long, and the rest are half as long as the first one. How many meters is the total length of these four bamboo poles?

1 + 1 △ 2 × 3 = 1 + 0.5 × 3 = 1 + 1.5 = 2.5 (m) a: the total length of the four bamboo poles is 2.5 meters