Assignment:
First part is to find an expression in terms of n, the results of the formula:
and prove the expression is correct?
Secondly
A Fibonacci sequence is the basis for a superfast calculation trick as follows:
Turn your back and ask someone to write down any two positive integers (vertically and one below the other). Ask them to add the two and get a third, put the third number below the second and add the last two numbers to get a fourth and so on until the column has ten numbers.
In other words you have 10 numbers of a generalised Fibonacci sequence, each the sum of the preceding two numbers except for the first two that are picked at random. You turn around, draw a line below the last two numbers and immediately write the sum of all 10 numbers. The secret is to multiply the seventh number by 11.
Develop a model for the calculation above, and prove mathematically that the sum of the first 10 numbers in a generalised Fibonacci sequence is always 11 times the seventh number.
Provide complete and step by step solution for the question and show calculations and use formulas.