Question

A function is defined by f(0)=1 and f(n)=f(n-1)+n+1. Find f(5)

Answer 1

f(5) = 21

Explanation:

Given:

`f(0)=1`

`f(n)=f(n-1)+n+1`

`\implies f(1)=f(0)+1+1=1 + 1 + 1=3`

`\implies f(2)=f(1)+2+1=3 + 2 + 1=6`

`\implies f(3)=f(2)+3+1=6+3+1=10`

`\implies f(4)=f(3)+4+1=10+4+1=15`

`\implies f(5)=f(4)+5+1=15+5+1=21`