JEE MATHEMATICS MCQ: MATHEMATICAL INDUCTION

1 Medium

1 of 1

Understanding +4 | -1

P\left( n \right)

is a statement

\left( {n \in N} \right)

such that, if

P\left( k \right)

is true,

P\left( {k + 1} \right)

is true for

k \in N

, then

p\left( n \right)

is true

View answer and explanation

Correct option: D

Nothing can be said

Option D (Nothing can be said) is correct because the base case P(1) must be proven true for the statement to be true for all 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}