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MissTica
3 years ago
15

What is the sum of the first five terms of the geometric series 3 − 6 + 12 − . . . ?

Mathematics
1 answer:
mezya [45]3 years ago
5 0

<span>3,−6,12,−24,...</span>

You can rewrite this as:

<span><span><span>(−1)</span>n</span>3⋅<span>(1,2,4,8,...)</span></span>

If we focus on <span>1,2,4,8...</span>

<span><span>a<span>n+1</span></span>=2<span>an</span></span>
with <span><span>a0</span>=1</span>.

This can be written out as a nice sum:
<span><span><span>N∑</span><span>n=0</span></span><span>2n</span>=<span>20</span>+<span>21</span>+<span>22</span>+<span>23</span>+...</span>
<span>=1+2+4+8+...</span>

Thus, now we can recombine everything to get:

<span>3<span><span>N∑</span><span>n=0</span></span><span><span>(−1)</span>n</span><span>2<span>n
</span></span></span>

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Write the prime factorization for 65,169
posledela

Let's try to find some primes that divide this number.

The number is not divisible by 2, because it is odd.

The number is divisible by 3 though, because the sum of its digits is:

6+5+1+6+9=27=3\cdot 9

So, we can divide the number by 3 and keep going with the factorization:

65169\div 3 = 21723

This number is again divisible by 3, because

2+1+7+2+3 = 15 = 3\cdot 5

We have

21723\div 3 = 7241

This number is no longer divisible by 3. Let's go on looking for primes that divide it: 5 doesn't because the number doesn't end in 0 nor 5. This number is not divisible by 7 or 11 either (just try). It is divisible by 13 though: we have

7241\div 13 = 557

And 557 is prime, so we're done. This means that the prime factorization of 65169 is

3^2\cdot 13 \cdot 557

8 0
3 years ago
jason built a rectangular tool shed that is 8 meters wide and has an area of 96 square meters. what is the length of jasons tool
pishuonlain [190]

Answer:

12 meters

Step-by-step explanation:

Area = length × width.  If we divided 96 (area) by 8 (width) we should get the length. 98 ÷  8 = 12.

6 0
3 years ago
WHOEVER gives the CORRECT answer FIRST, gets brainliest answer and thanks
Alex_Xolod [135]
Yes, because they are similar(or you can call congruent), proved by SAS or simply HL.
7 0
3 years ago
Read 2 more answers
What is the solution to 2x^2+8x=x^2-16?<br> x=4<br> x=22<br> x=2<br> x=4
Taya2010 [7]

Answer:

x = -4

Step-by-step explanation:

2x² + 8x = x² - 16

x² + 8x + 16 = 0

x² + 4x + 4x + 16 = 0

x(x + 4) + 4(x + 4) = 0

(x + 4)² = 0

x = -4

4 0
3 years ago
Read 2 more answers
Justify your reasoning
love history [14]

Answer:

Yes

Step-by-step explanation:

You can conclude that ΔGHI is congruent to ΔKJI, because you can see/interpret that there all the angles are congruent with one another, like with vertical angles (∠GIH and ∠KIJ) and alternate interior angles (∠H and ∠J, ∠G and ∠K).

We also know that we have two congruent sides, since it provides the information that line GK bisects line HJ, meaning that they have been split evenly (they have been split, with even/same lengths).

<u><em>So now we have three congruent angles, and two congruent sides. This is enough to prove that ΔGHI is congruent to ΔKJI,</em></u>

<u><em /></u>

7 0
3 years ago
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