CBSE Class 6 Mathematics
Question 15 of 25
Patterns in Mathematics — Question 17
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Question What happens when you start to add up powers of 2 starting with 1, i.e., take 1, 1 + 2, 1 + 2 + 4, 1 + 2 + 4 + 8,…..? Now add 1 to each of these numbers — what numbers do you get? Why does this happen?
Let us add powers of 2 starting with 1
Here 1 = 1
1 + 2 = 3
1 + 2 + 4 = 7
1 + 2 + 4 + 8 = 15
1 + 2 + 4 + 8 + 16 = 31
Hence series 1, 3, 7, 15, 31,….. is formed.
Now let us add 1 to each of the above numbers
1 + 1 = 2 = 2
1
1 + 2 + 1 = 4 = 2 × 2 = 2
2
1 + 2 + 4 + 1 = 8 = 2 × 2 × 2 = 2
3
1 + 2 + 4 + 8 + 1 = 16 = 2 × 2 × 2 × 2 = 2
4
This happens because we are adding (1 + 1 = 2), hence the power of 2 increases.