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lina2011 [118]
3 years ago
12

Can somebody prove this mathmatical induction?

Mathematics
1 answer:
Flauer [41]3 years ago
4 0

Answer:

See explanation

Step-by-step explanation:

1 step:

n=1, then

\sum \limits_{j=1}^1 2^j=2^1=2\\ \\2(2^1-1)=2(2-1)=2\cdot 1=2

So, for j=1 this statement is true

2 step:

Assume that for n=k the following statement is true

\sum \limits_{j=1}^k2^j=2(2^k-1)

3 step:

Check for n=k+1 whether the statement

\sum \limits_{j=1}^{k+1}2^j=2(2^{k+1}-1)

is true.

Start with the left side:

\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}\ \ (\ast)

According to the 2nd step,

\sum \limits_{j=1}^k2^j=2(2^k-1)

Substitute it into the \ast

\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}=2(2^k-1)+2^{k+1}=2^{k+1}-2+2^{k+1}=2\cdot 2^{k+1}-2=2^{k+2}-2=2(2^{k+1}-1)

So, you have proved the initial statement

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What is 7 7/9 divided by 4/7
e-lub [12.9K]

Answer:

4 44/49

Step-by-step explanation:

7 7/9 is 70/9

then u use 70/9 multiply by 7/4(I call it keep, change, flip method for division of fraction)

You keep the 1st fraction and because it is a mixed fraction, changing it to improper fraction is easier to solve it later on.

after that, you change the division sign to multiply sign(÷ to ×)

then you flip the 2nd fraction, which means 7/4 becomes 4/7

So overall it becomes 60/7 × 4/7 =240/49,4 44/49 as a mixed fraction.

Answer is 4 44/49

5 0
3 years ago
Needing help, the secretary of the united states department of agriculture asked your teacher, "if a chicken-and-a-half can lay
Flura [38]

we are given that

3 chickens to lay 32 eggs

now, we can find number of eggs per chicken

number of eggs per chicken= (total eggs)/(total chicken)

so, we get

number of eggs per chicken is

=\frac{32}{3}

now, we can set up following

1.5 chicken : 1.5 eggs : 1.5 days  

3 chickens : 3 eggs : 1.5 days  

1 chicken : 1 egg : 1.5 days

Since, changing number of chicken won't affect time

time to lay eggs will always remain same

so,

for 1 chicken to lay =\frac{32}{3} eggs

it takes

=\frac{32}{3}*1.5 days

=16 days..............Answer


8 0
2 years ago
Divide: 6 ÷ 1/2=12
schepotkina [342]
I believe the answers are:
1. Twelve circles
2. Two equal parts
3. 6 parts would be shaded
6 0
2 years ago
Read 2 more answers
Select all the correct answers.
sukhopar [10]

Answer:

Second point (-5/2, -7/2)

First point (3/2, 17/2)

Step-by-step explanation:

We have two equations, and we want to know at wich poin are equal. Hence, we have a system of equations and the solution is nothing more that the point (x,y) where those functions intercepts.

4x2+ 7x -11=y

3x+4=y

Lets use substitute method

4x2+7x-11=3x+4

This can be re arrange as the following eq:

4x2+4x-15=0

A quadratic equation, its solution can be obtained using the below eq.

x=\frac{-b+/- \sqrt{x^{2}-4ac } }{2a}

where a=4, b=4, c=-15.

Remember, the quadratic equation as a +/- sign, meaning that you will obtain one answer using the + operator and other using the - operator.

By doing the above, we have x=-5/2 and x=3/2

By using x=3/2 in equation of line (3x+4=y)  we have y=17/2

First point (3/2, 17/2)

By using x=-5/2 in equation of line (3x+4=y) we have y= -7/2

Second point (-5/2, -7/2)

Those points are the ones where the line and the parabola intercept.

7 0
3 years ago
HELP ITS URGENT WILL MARK BRAINLEST
sesenic [268]
= 16 * 10^13

which in scientific notation is  1.6 * 10^14
7 0
3 years ago
Read 2 more answers
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