Question

Topic: Recursion
Using recursion, write a program that returns the sum of the following series.
$\tt 0+2+18+72+... + nth \: term$
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#Challenge​

Answer 1

Hint:

For this series:

$\rm\longrightarrow n^{th}\ term=\dfrac{[n(n-1)]^{2}}{2}$

The Co‎de:

The problem is solved using Python.

f=lambda x: (x*(x-1))*‎*2//2   # defines f(x)

sum=lambda n:f(n)+sum(n-1) if n else 0   # defines sum(n)

n=int(input('Enter limit: '))  # accepts limit.

print(f'Sum of first {n} terms of the series is {sum(n)}.')   # displays sum.

Algorithm:

The sum can be calculated using the following recursive algorithm.

$\rm\longrightarrow sum(n) = \begin{cases}\rm f(n)+sum(n-1), \ \ n>0\\ \rm0,\ \ n=0\end{cases}$

Where f(n) denotes the nᵗʰ term of the series, given by:

$\rm\longrightarrow f(n)=\dfrac{[n(n-1)]^{2}}{2}$

See attachment for output.