Collapsing sequence
Okay kiddo, have you ever played with those stacking cups? You put them on top of each other and make a tower. But sometimes, you can make the tower collapse by pulling one cup out from the bottom. That's what a collapsing sequence is in math!
Imagine we have a long list of numbers, like 1, 2, 3, 4, 5, 6, 7. We can "collapse" this sequence by taking the sum of every two adjacent numbers. So we'd get 3, 5, 7, 9, 13.
Then we do it again by taking the sum of the adjacent pairs: 8, 12, 16, 22. And again: 20, 28, 38. Keep going until you're left with just one number, that's the "collapsed" sequence!
It's like pulling out the bottom cup from the tower - we're reducing the sequence bit by bit until it can't be reduced any further. And just like how the tower falls down when you pull out the bottom cup, the sequence "falls" into one final number when we collapse it.
Imagine we have a long list of numbers, like 1, 2, 3, 4, 5, 6, 7. We can "collapse" this sequence by taking the sum of every two adjacent numbers. So we'd get 3, 5, 7, 9, 13.
Then we do it again by taking the sum of the adjacent pairs: 8, 12, 16, 22. And again: 20, 28, 38. Keep going until you're left with just one number, that's the "collapsed" sequence!
It's like pulling out the bottom cup from the tower - we're reducing the sequence bit by bit until it can't be reduced any further. And just like how the tower falls down when you pull out the bottom cup, the sequence "falls" into one final number when we collapse it.
Related topics others have asked about: