Exercise 7.2

Exercise 7.2#

Question 1#

Calculate the following sum using a for loop:

\sum_{i = 0}^{50} 3 i^{2} + i

(The answer is $130050$ )

Question 2#

Find and print the first $10$ terms of the following recursive series using a for loop:

\begin{aligned} T_{0} & = 0 \\ T_{n} & = T_{n - 1} + 3 \end{aligned}

Question 3#

Write some code that takes a string as an input and prints it out with spaces inserted between each character. Make sure not to insert spaces before and after the string.

Question 4#

Write some code that will calculate the Taylor series expansion of $e^{x}$ , using the first $N$ terms. Both $N$ and $x$ must be provided by the user. Remember:

$e^{x} = 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + \frac{x^{4}}{4!} + \dots + \frac{x^{N}}{N!}$

Hint: You could use math.factorial OR you could calculate a running factorial in the loop.
Bonus: modify your code above to print out the solution in the form:
“e^5 = 1 + 5 + 5^2 /2! + 5^3 /3! + 5^4 /4! = 65.375”
where the user has chosen $x = 5$ and $N = 4$ in this example (make your code work in the general case).