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sam_pi

  • one year ago

is this a combination problem ? 1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 . . . The number above begins with a "1", then continues "12," "123," "1234," and so on until the number "9" is reached. How many digits are in the final number? A. 36 B. 40 C. 45 D. 54 E. 81 Correct Answer: C i know the solution is to add the numbers together and then you get 45 , but i don’t understand why ? why should we add the numbers together instead of multiplying ? what type of problem is this ? is this a combination problem ?

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  1. mathstudent55
    • one year ago
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    |dw:1441134332425:dw|

  2. mathstudent55
    • one year ago
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    The number of digits until you reach 9 is the sum of 1 + 2 + 3 + 4 + 5 + ... + 9 It is the sum of an arithmetic series that starts at 1, ends at 9, and has common difference 1.

  3. mathstudent55
    • one year ago
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    This is not a combination problem. It is a sum of an arithmetic sequence.

  4. mathstudent55
    • one year ago
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    \(\large S_n = \dfrac{a_{n } + a_{n+1}}{2} \) To sum all the numbers in an arithmetic sequence, multiply the last number by the next one, and divide by 2.

  5. mathstudent55
    • one year ago
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    To sum 1 + 2 + 3 + 4 + 5 + ... + 9, first find the next number. It is 10. Multiply 9 by 10 and divided by 2.

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