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 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 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
Here are a few: An integer is a counting number, or a whole number. If you have a negative counting number, zero, or a positive counting number, you have an integer, and any integer will be a member of one of those three sets of numbers. Zero is the only integer that is neither positive or negative. Each integer (except zero) has a compliment with an opposite sign.
It is the smallest positive integer which is a multiple of the denominators of each fraction.