The output will be: You owe $ 15.0
Answer:
B. Symmetric key encryption
Explanation:
Symmetric key encryption is one in which a single encryption key is sent to the receiver so both sender and receiver share the same key. In this type of encryption, the sender uses a particular key to encrypt the data and sends the encrypted data (cipher data) to the receiver and then the receiver uses the same key to decrypt the data.
Public key encryption, or asymmetric encryption uses two keys - a private key and a public key. The public key is know to everyone while the private key is known only to those for whom the message is intended. An application of this type of encryption is in SSL (Secure Sockets Layer) - a protocol for transmitting data privately on the internet.
Private key encryption is not exactly one of the encryption methods but rather, a private key and a public key are used in encryption.
The best option is therefore <em>symmetric key encryption</em>.
<em>Hope this helps!</em>
The recursive function would work like this: the n-th odd number is 2n-1. With each iteration, we return the sum of 2n-1 and the sum of the first n-1 odd numbers. The break case is when we have the sum of the first odd number, which is 1, and we return 1.
int recursiveOddSum(int n) {
if(2n-1==1) return 1;
return (2n-1) + recursiveOddSum(n-1);
}
To prove the correctness of this algorithm by induction, we start from the base case as usual:
by definition of the break case, and 1 is indeed the sum of the first odd number (it is a degenerate sum of only one term).
Now we can assume that 
returns indeed the sum of the first n-1 odd numbers, and we have to proof that 
returns the sum of the first n odd numbers. By the recursive logic, we have
and by induction, is the sum of the first n-1 odd numbers, and 2n-1 is the n-th odd number. So, is the sum of the first n odd numbers, as required:
