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docker41 [41]
3 years ago
12

Compute

i+i^2+i^3+\cdots+i^{258}+i^{259}" alt="i+i^2+i^3+\cdots+i^{258}+i^{259}" align="absmiddle" class="latex-formula">.
Mathematics
2 answers:
artcher [175]3 years ago
7 0

9514 1404 393

Answer:

  -1

Step-by-step explanation:

Alternate terms have a sum of zero:

  i^n +i^(n+2) = (i^n)(1 +i^2) = (i^n)(1 -1) = 0

So, the sum to i^256 is zero, and i^257 +i^259 = 0. The value of the sum is then i^258 = i^(258 mod 4) = i^2 = -1

The given expression evaluates to -1.

xz_007 [3.2K]3 years ago
3 0

Answer:

-1

Step-by-step explanation:

Note that i+i^2+i^3+i^4 = i-1-i+1 = 0, and this means that every 4 terms, the terms cancel to 0. Therefore, by taking modulo 4, we only need to find i^{257}+i^{258}+i^{259} = i-1-i = -1 since $i$ has a cycle of 4.

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djverab [1.8K]
The last number will either be 5 or 0. For example 15, or 20.
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3 years ago
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To describe a specific arithmetic sequence, Elijah wrote the recursive formula:
Rufina [12.5K]

Answer:

Y(n) = 7n + 23

Step-by-step explanation:

Given:

f(0) = 30

f(n+1) = f(n) + 7

For n=0 : f(1) = f(0) + 7

For n=1 :  f(2) = f(1) + 7

For n=2 : f(3) = f(2) + 7 and so on.

Hence the sequence is an arithmetic progression with common difference 7 and first term 30.

We have to find a general equation representing the terms of the sequence.

General term of an arithmetic progression is:

T(n) = a + (n-1)d

Here a = 30 and d = 7

Y(n) = 30 + 7(n-1) = 7n + 23

7 0
3 years ago
Solve the following equation for x. x = -2 x = 2 x = -17 x = -7 (x - 5)/2 = -6
nordsb [41]

Step-by-step explanation:

x= -2,

(x - 5) / 2= -6

( (-2) - 5) / 2= -6

(-7) / 2 = -6

-3.5 = - 6

right hand side not equal to left hand side of this equation.so,x= -2 cannot exist for this equation.

x=2,

(x - 5) / 2= -6

(2 - 5) / 2= -6

(-3) / 2= -6

-1.5 = - 6

right hand side not equal to left hand side of this equation.so,x= 2 cannot exist for this equation.

x= -17

(x - 5) / 2= -6

( ( -17) - 5) / 2= -6

(- 22) / 2= -6

-11 = -6

right hand side not equal to left hand side of this equation.so,x= -17 cannot exist for this equation.

x= -7,

(x - 5) / 2= -6

( ( -7) -5) / 2= -6

(-12) / 2= -6

-6= -6

right hand side equal to left hand side of this equation.so,x= -7 exist for this equation.

8 0
3 years ago
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PIT_PIT [208]
D
It makes sense. At most means equal or less than. The 10 per hour has a variable.
8 0
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A) Work out the value of 19 + 7 divided by 2-5
agasfer [191]

Answer: -8.66666666667

Step-by-step explanation: Do it step by step. So 19+7= 26

Then 2-5= 3

So 26 divided by -3 = -8.66666666667

8 0
3 years ago
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