JEE MATHEMATICS MCQ: MATHEMATICAL INDUCTION

1 Medium

1 of 1

Application +4 | -1

Statement

p(n): 3^{2 n+1}+2^{n-1}, \forall \, n \in \mathrm{N}

is divisible by

View answer and explanation

Correct option: C

Option C is correct. Using mathematical induction, it can be shown that the expression 3⁽²ⁿ⁺¹⁾ + 2^(n-1) is divisible by 7 for all n in N.

More Questions from MATHEMATICAL INDUCTION

Practice All Chapter MCQs →

\frac{1^2}{3}+\frac{1^2+2^2}{5}+\frac{1^2+2^2+3^2}{7}+\ldots

n

P\left( n \right):2 + 4 + 6 \ldots + \left( {2n} \right),\;n \in N,

\begin{array}{l} P\left( k \right) = k\left( {k + 1} \right) + 2\mathrm{implies}\\ P\left( k \right) = \left( {k + 1} \right)\left( {k + 2} \right) + 2 \end{array}

k \in N.

P\left( n \right) = n\left( {n + 1} \right) + 2

n

n

a\left( n \right) = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ... + \frac{1}{{\left( {{2^n}} \right) - 1}}.

n(n+1)(n+2)(n+3)

n \in N

12 {~N}

8 {~m}

6 {~m}