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Powerful Number Patterns

Here are some number patterns all involving the sum of neighbouring numbers (consecutive numbers). Can you spot the patterns here? Hint: why are they called powerful number patterns?

1= ?
1+2+1= ?
1+2+3+2+1= ?
1+2+3+4+3+2+1= ?
1+2+3+4+5+4+3+2+1= ?
1+2+3+4+5+6+5+4+3+2+1= ?
......

The second number pattern goes in pairs, where the second of each pair extends the first in the pair: so, for example, 2+3+4 is the first of a pair and the second extends it to 2+3+4+5+6+7.

1
1+2
= ?
= ?
2+3+4
2+3+4+5+6+7
= ?
= ?
5+6+7+8+9+10+11+12+13
5+6+7+8+9+..+20+21+22
= ?
= ?
14+15+...+39+40
14+15+...+?
= ?
= ?

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Patterns