One day a king left his castle with a bag of silver coins to wander his kingdom. to the first peasant he met, he gave half his coins plus two more. a little later, he met another peasant to whom he also gave half his coins plus two more. walking on, he met a third peasant and again gave half his coins plus two more. finally, the king went home with two coins left in his bag.

(a) how many coins did he have to begin with?

(b) what if he was left with "n" amount of coins?

(c) what if he gave away any unit fraction (1/a) each time?

(d) what if he gave away any unit fraction (1/a) each time and was left with any amount of coins (d)?

Step-by-step explanation:

Let us assume the king before leaving his castle had x silver coins.

For the first peasant he met he gave

Now he is left with

Next peasant he gave half of what he had and two more

Hence next peasant got

Balance left =

Third peasant got half + 2 more

Hence third peasant got

Balance he had

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column