Prove by method of induction, for all $n \in N$: $3^n - 2n - 1$ is divisible by $4$.

Prove by method of induction, for all n ∈ N: 3ⁿ - – Class 11 Mathematics

EXERCISE 4.1 · Q12

n \in N

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Let $P(n):3^n-2n-1=4m$ . Base: $n=1$ : $3-2-1=0=4(0)$ ; divisible by 4 (0 counts as a multiple), so holds. Hypothesis: assume $3^k-2k-1=4a$ , i.e. $3^k=4a+2k+1$ . Step: $3^{k+1}-2(k+1)-1=3\cdot3^k-2k-3=3(4a+2k+1)-2k-3=12a+6k+3-2k-3=12a+4k=4(3a+k)$ , a mu …

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Q.Prove by method of induction, for all $n \in N$ : $3^n - 2n - 1$ is divisible by $4$ .

Concept understanding — Principle of Mathematical Induction

Q.Prove by method of induction, for all n∈Nn \in Nn∈N: 3n−2n−13^n - 2n - 13n−2n−1 is divisible by 444.

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Q.Prove by method of induction, for all $n \in N$ : $3^n - 2n - 1$ is divisible by $4$ .

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