ISRO CS 2017 | Question 39

This question is from the ISRO CS 2017 examination. It tests your understanding of recursion and mathematical concepts.

Problem statement

Suppose f(0) = 1, f(1) = 2, ..., f(n) = n+1 for some n >= 0. If g(n) = f(0) + f(1) + ... + f(n), then find the value of g(15).

Solution

We can use recursion to solve this problem. Notice that the function f(n) can be defined recursively as follows:

f(0) = 1
f(n) = n+1 for n > 0

Similarly, the function g(n) can be defined recursively using the formula g(n) = g(n-1) + f(n). We can use this formula to compute g(15) recursively as follows:

g(0) = f(0) = 1
g(n) = g(n-1) + f(n) for n > 0

We can write this function in Python as follows:

def f(n):
    if n == 0:
        return 1
    else:
        return n + 1

def g(n):
    if n == 0:
        return f(0)
    else:
        return g(n-1) + f(n)

print(g(15)) # Output: 136

The function f(n) simply returns n+1 for n > 0 and 1 for n = 0. The function g(n) uses recursion to compute the sum of f(i) for i from 0 to n. We can then call this function with 15 as the argument to compute the final answer.

The output of the above program is 136, which is the value of g(15).

Conclusion

In this article, we have seen how to use recursion to solve a math problem. We used the formula g(n) = g(n-1) + f(n) to compute the sum of f(i) for i from 0 to n. We then implemented this formula in Python and computed the value of g(15).