1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
vovangra [49]
3 years ago
13

Find S^20 if the series 1 + 1.1 ..... is a (a) arithmetic (b) geometric

Mathematics
1 answer:
quester [9]3 years ago
7 0
I'm guessing S^20 is actually referring to the 20th partial sum S_{20}, with

S_{20}=1+(1+1\times0.1)+(1+2\times0.1)+\cdots+(1+18\times0.1)+(1+19\times0.1)

in the arithmetic case, and

S_{20}=1+1.1+1.1^2+\cdots+1.1^{18}+1.1^{19}

in the geometric case.

(a) Combining like terms, we have

S_{20}=20+0.1(1+2+\cdots+18+19)

and invoking the formula

1+2+\cdots+(n-1)+n=\dfrac{n(n+1)}2

we end up with

S_{20}=20+0.1\dfrac{19\times20}2=39

(b) Multiply S_{20} by 1.1, then subtract this from S_{20}:

1.1S_{20}=1.1+1.1^2+1.1^3+\cdots+1.1^{19}+1.1^{20}

S_{20}-1.1S_{20}=-0.1S_{20}=1-1.1^{20}
\implies S_{20}=\dfrac{1.1^{20}-1}{0.1}\approx57.275
You might be interested in
What is the answer plz
Bumek [7]

Answer:

9 days

Step-by-step explanation:

He sets his watch 12 seconds behind

For every day that passes it falls back another 1 second

So once it is 21 seconds behind all you have to do is subtraction to find the amount of days past

21 - 12 = 9

Since its 12 seconds behind already itll take 9 days to be behind 9 more seconds.

6 0
3 years ago
Probability cards <br> How to solve this, I don’t get it all all?
Ronch [10]
There are 12 cards with different letters & patterns. The probability of randomly choosing [random card] is #[random card]/total cards.

Think of that as ratio as a %chance or probability of written as P(X). The question says to write the %chance as a fraction.

1) 2/12 = 1/6
2) 2/12 = 1/6
3) 0/12 = 0
4) 12/12 = 1
5) This is tricky. M & T would imply one card with both letters on it. 0/12 = 0
6) 4/12 = 1/3
7) 6/12 = 1/2
8) 5/12
9) 3/12 = 1/4
10) 8/12 = 2/3
11) 10/12 = 5/6
12) Odds = [favorable]:[unfavorable] = 5:7
3 0
2 years ago
Planes have edges true or false
Cerrena [4.2K]
False planes do not have edges.
6 0
3 years ago
14. In a right triangle, if one acute angle has measure 10x + 6 and the other has measure 2x + 7, find the larger of these two a
lubasha [3.4K]

Answer:

421/6 degrees

Step-by-step explanation:

The acute angles of a right triangle are complementary, so

10x+6+2x+7=90 \\ \\ 12x+13=90 \\ \\ 12x=77 \\ \\ x=\frac{77}{12}

So, the acute angles measures 421/6 degrees and 119/6 degrees, and thus the larger angle is 421/6 degrees.

7 0
1 year ago
CAN ANYONE ANSWER THIS CORRECTLY???
Alisiya [41]
B, D, E are appropriate choices.

_____
A ray can be named by its (one) end-point and any other point on the ray. Since there are an infinite number of points on the ray, it can be named an infinite number of ways.
4 0
3 years ago
Other questions:
  • A model of an apartment is shown where 1/4 inch represent 3 feet in the actual ap
    5·1 answer
  • Identify the pattern in the list of numbers. Then use this pattern to find the next number.
    10·2 answers
  • Jakob is asked to simplify the expression –3a + 4b + 5a + (–7b).
    10·1 answer
  • 12/11-(-2/3)=?????????????????????????????????????????
    8·2 answers
  • Please help me with this problem​
    14·1 answer
  • What is the range of Y = log8X?
    7·2 answers
  • Consider the function ƒ(x) = x2. Which of the following functions shifts ƒ(x) downward 5 units and to the right 3 units?
    5·1 answer
  • Please help me............................
    6·1 answer
  • The sum of two numbers is 10 and the difference is six. what are the numbers? create the equation and graph.
    12·1 answer
  • A restaurant chef wants to install a new floor in his kitchen. The kitchen measures 8 yards wide and 12 yards long, and the floo
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!