Question 46

Mathematics Binomial Expansions (Theorem) Medium

According to the principle of mathematical induction. If \( P(k+1)= \) \( m^{(k+1)}+5 \) is true, then \(\ldots\)\(\ldots\) must be true?

(A) \( P(K)=3 ~m^{(k)} \)
(B) \( P(k)=m^{(k)}+5 \)
(C) \( P(k)=m^{(k+2)}+5 \)
(D) \( P(k)=m^{(k)} \)
View Dynamic Solution & Explanation
Correct Solution: Option B

Step-by-step Solution:

According to the principle of mathematical induction, if \( P(k+1) = m^{(k+1)} + 5 \) is true, then which of the following must also be true? \[\] The expression \( P(k+1) = m^{(k+1)} + 5 \) \(\implies\) that when traced back to ( P(k) ), it follows that \( P(k) = m^{(k)} + 5 \). \[\] \[\] Correct Option: (b)