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vhife4901
07.12.2021 •
Mathematics
Can you please explain this one^
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Ответ:
The solutions for 1 + 3 + 5 +...+ (2n - 1), for the first 10 natural numbers are given in the explanation section below.
Step-by-step explanation:
To calculate 1 + 3 + 5 +...+ (2n - 1) for several natural numbers n, we will use several natural numbers to represent n.
For n= 1,
2n - 1 = 2(1) - 1 = 2 - 1 = 1
Hence, 1 = 1
For n = 2,
2n - 1 = 2(2) - 1 = 4 - 1 = 3
Hence, 1 + 3 = 4
For n = 3,
2n - 1 = 2(3) - 1 = 6 - 1 = 5
Hence, 1 + 3 + 5 = 9
For n = 4,
2n - 1 = 2(4) - 1 = 8 - 1 = 7
Hence, 1 + 3 + 5 + 7 = 16
For n = 5,
2n - 1 = 2(5) - 1 = 10 - 1 = 9
Hence, 1 + 3 + 5 + 7 + 9 = 25
For n = 6,
2n - 1 = 2(6) - 1 = 12 - 1 = 11
Hence, 1 + 3 + 5 + 7 + 9 + 11 = 36
For n = 7,
2n - 1 = 2(7) - 1 = 14 - 1 = 13
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
For n = 8,
2n - 1 = 2(8) - 1 = 16 - 1 = 15
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64
For n = 9,
2n - 1 = 2(9) - 1 = 18 - 1 = 17
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81
For n = 10,
2n - 1 = 2(10) - 1 = 20 - 1 = 19
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100