First, the answer:
a-sub-n = [2n - 1 - (-1)^n+1]/4.
Now, the reasoning:
Each term = n - (1/n) - (1/2 for odd n's, 0 for even n's).
The formula for the alternating 1/2's and 0's is [1 + (-1)^n+1]/4
Simplification leads to the answer first given above.
In an arithmetic sequence the same number (positive or negative) is added to each term to get to the next term.In a geometric sequence the same number (positive or negative) is multiplied into each term to get to the next term.A geometric sequence uses multiplicative and divisive formulas while an arithmetic uses additive and subtractive formulas.
A Fibonacci number, Fibonacci sequence or Fibonacci series are a mathematical term which follow a integer sequence. The first two numbers in Fibonacci sequence start with a 0 and 1 and each subsequent number is the sum of the previous two.
Each digit is repeated the number of times equal to its value. 1 22 333 4444 55555 666666 7777777 88888888 999999999
The given series is known as a sequence of perfect cubes with alternating signs. The rule for this series is that each term is the cube of the next integer in the sequence, alternating between positive and negative. In this case, the series starts with -1, then continues with 2^3 = 8, -3^3 = -27, 4^3 = 64, and -5^3 = -125.
Half off each time, alternating positive and negative, the next number would be 6.25
An integer (not interger!) sequence is an ordered set of numbers such that each number in the set is an integer, or a whole number.
The LCM of a set of integers is the smallest positive integer which each of them will divide evenly.An alternative characteristic is that it is the smallest positive integer which is in the times-table of each of the numbers.
No, a sequence does not necessarily imply repetition. A sequence is a particular order in which related elements follow each other, but they do not have to be repeated. Each element in a sequence is unique and follows a specific pattern or rule.
The sequence 1, 3, 5, 7, 9 is an arithmetic sequence where each term increases by 2. The nth term can be expressed as ( a_n = 2n - 1 ). Therefore, for any positive integer ( n ), the nth term of the sequence is ( 2n - 1 ).
The first 100 positive odd integers are the numbers that can be expressed in the form of (2n - 1), where (n) is a positive integer. They start from 1 and go up to 199. Specifically, the sequence is: 1, 3, 5, 7, ..., up to 199. Each subsequent odd integer is obtained by adding 2 to the previous one.
There is no such number. According to Peano's axiom, each positive integer has a successor, which is larger (one more) than it. So the set of integers goes on for ever.
2520
Should be 50! Every odd integer is 1 less than the corresponding even integer and there are 50 of each in 100...
To create the five-pointed logo, the sequence needs to be repeated once for each point of the star. Therefore, the sequence is typically repeated five times. Each repetition corresponds to forming one of the star's points. This repetition allows for the full structure of the five-pointed star to be completed.
To design a counter for a repeated binary sequence, first determine the specific sequence you want to repeat, such as "0101." You can use a finite state machine (FSM) with states representing each bit in the sequence. Each state transition occurs on a clock pulse, cycling through the sequence until it resets. Implement this using flip-flops and combinational logic to ensure the output follows the desired binary pattern.
In an arithmetic sequence the same number (positive or negative) is added to each term to get to the next term.In a geometric sequence the same number (positive or negative) is multiplied into each term to get to the next term.A geometric sequence uses multiplicative and divisive formulas while an arithmetic uses additive and subtractive formulas.
what is least positive integer that is divisible by each of the integers 1 through 7 inclusive ? a 420 b 840 c 1260 d 2520 e 5o40