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Naddika [18.5K]
3 years ago
12

Given the proposition,

Mathematics
1 answer:
zubka84 [21]3 years ago
6 0

Answer and Explanation:

Given : P(n): 1 + 2 + 2^2 + 2^3 + . . . + 2^n = 2^{n+1} - 1, n=0,1,2,..

To find : The values of following expression ?

Solution :

The function is P(n)=2^{n+1} - 1

1) Value of P(0),

P(0)=2^{0+1} - 1

P(0)=2^{1} - 1

P(0)=2 - 1

P(0)=1

2) Value of P(1),

P(1)=2^{1+1} - 1

P(1)=2^{2} - 1

P(1)=4- 1

P(1)=3

3) Value of P(2),

P(2)=2^{2+1} - 1

P(2)=2^{3} - 1

P(2)=8- 1

P(2)=7

4) Value of P(n+1),

P(n+1)=2^{n+1+1} - 1

P(n+1)=2^{n+2} - 1

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4 years ago
Which equation is equal up to one-hundredth of 36? Is it 0.3*0.12 or 0.36÷0.12 or 0.3*1.2
Mumz [18]
Its 360 beacuse u multiply all of those numbers


3 0
3 years ago
Read 2 more answers
Compute the sums below. (Assume that the terms in the first sum are consecutive terms of an arithmetic sequence.)
riadik2000 [5.3K]

Answer:

=18975

Step-by-step explanation:

This is an arithmetic sequence

an = a1 +d(n-1)

a1 =9

d = 12-9 = 3

an = 9 +3 (n-1)

The sum of an arithmetic sequence is given by

Sn = n/2 (a1+an)

So we need to determine what number in the sequence 336 is

an = 9 +3 (n-1)

336 = 9 +3(n-1)

Subtract 9 from each side

336-9 =9+-9 + 3(n-1)

327 = 3(n-1)

Divide each side by 3

327/3 =3/3(n-1)

109 = n-1

Add 1 to each side

109+1= n-1+1

110 = n

336 is the 110  term

The sum from 9 to 336

Sn = n/2 (a1+an)

S 110 = 110/2 (9+336)

          = 55 (345)

          =18975

5 0
3 years ago
What is the x-intercept of the line 4x+3y=36
Genrish500 [490]

we can always find the x-intercept of any equation by simply setting y  = 0, so let's do so

\bf 4x+3y=36\implies 4x+3(\stackrel{y}{0})=36\implies 4x=36\implies x=\cfrac{36}{4}\implies x = 9 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (9~~,~~0)~\hfill

4 0
4 years ago
find the 17th term of the arithmetic sequence whose common difference is d=3 and whose first term is a1=5.
miskamm [114]

Answer:56

Step-by-step explanation:

7 0
3 years ago
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