Series - Questions
🔒 Unlock Full Access
You're currently viewing a preview. Sign up or log in to access all 11 questions and complete solutions.
Question 1
11864
To prove by mathematical induction that \(1 + 3 + {3^2} + ....... + {3^{n - 1}} = \dfrac{{{3^n} - 1}}{2}\) it is assumed that \(1 + 3 + {3^2} + ....... + {3^{k - 1}} = \dfrac{{{3^k} - 1}}{2}\) and then it is required to show that \(\dfrac{{{3^k} - 1}}{2} + {3^k} = \)
\(\dfrac{{{3^k} - 1}}{2}\)
\(\dfrac{{{3^{k + 1}} - 1}}{2}\)
\(\dfrac{{{3^{k + 1}} + 1}}{2}\)
\(\dfrac{{{3^k} + 1}}{2}\)
📚 Want More Questions?
There are 10 more questions available. Create your free account to access the complete question set with detailed solutions.