Mathematics Crash Course JEE Main>Chapter 17 - Mathematical Induction>Level 1>Q 5

EASY

JEE Main

IMPORTANT

Earn 100

Using mathematical induction, the numbers $a_{n}$ 's are defined by $a_{0} = 1, a_{n + 1} = 3 n^{2} + n + a_{n}, (n \geq 0)$ , then $a_{n} =$

55.56% studentsanswered this correctly

Important Questions on Mathematical Induction

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 17 - Mathematical Induction>Level 1>Q 6

If

a_{n} = \sqrt{7 + \sqrt{7 + \sqrt{7 + ......}}}

having

n

radical signs, then by methods of mathematical induction which of the following is true?

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 17 - Mathematical Induction>Level 1>Q 8

If

P (n) : 1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16} + \dots + \frac{1}{n^{2}} < 2 - \frac{1}{n}

is true and

n \in N,

then

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 17 - Mathematical Induction>Level 1>Q 9

For all

n \in N, 2 \cdot 4^{2 n + 1} + 3^{3 n + 1}

is divisible by

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 17 - Mathematical Induction>Level 1>Q 10

If

P (n) : 2 + 4 + 6 + ... + (2 n), n \in N

then

P (k) = k (k + 1) + 2

implies

P (k + 1) = (k + 1) (k + 2) + 2

is true for all

k \in N

. So, the statement

P (n) = n (n + 1) + 2

is true for