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steposvetlana [31]
3 years ago
11

The sum of the first 46 postive and odd numbers is

Mathematics
1 answer:
atroni [7]3 years ago
3 0

The sum of first 46 positive and odd numbers is 2116

<em><u>Solution:</u></em>

Given that we have to find the sum of first 46 positive and odd numbers

<em><u>The sum of first "n" natural odd numbers which are positive is given as:</u></em>

Sum = n^2

Here, n = 46

Therefore,

sum of first 46 positive and odd numbers = 46^2

sum of first 46 positive and odd numbers = 46 \times 46 = 2116

Thus the sum of first 46 positive and odd numbers is 2116

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If the given number is in base 2, that means

11100111₂ = 2⁷ + 2⁶ + 2⁵ + 2² + 2 + 1

8 = 2³, and so we have

11100111₂ = 2 • (2³)² + (2³)² + 2² • 2³ + 2² + 2 + 1

11100111₂ = 3 • 8² + 4 • 8 + 7

11100111₂ = 347₈

Because 8 is the 3rd power of 2, we can also split up the given number into block of length up-to 3, then convert each block directly into base 8:

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11₂ = 2 + 1 = 3

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so again we get 347₈.

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