Show that 2^2n-1 +1 is divisible by 3 for all n > 1.

The proof makes use of congruences as follows:

Step-by-step explanation:

We can prove this result using congruences module 3. First of all we shall show that

for all . By induction we have

Then induction we proved that for all . Then

From here we conclude that the expression is divisible by 3.

$53.50

step-by-step explanation:

you have to subtract the amount of money chuck earned ($72.50) by the cost of the gas for the mower ($11.25) and the new string for the trimmer he bought ($7.75).

72.50-11.25=61.25

and then subtract $61.25 by the second thing he bought (the new string for the trimmer)

61.25-7.75=53.5

so in total it's $53.50 (53 dollars and 50 cents)

1. 8

2. 9

3. 20

4. 3

5. 17

6. 2.2

7. 11.25

8. 1

9. 14

10. 2

step-by-step explanation:

thats the first half