Question

Prove that 2n>n for all positive integers n .​

Answer 1

Answer:

P=Rs.1200,A=Rs.1632,t=4

A=P+

100

P×r×t

⟹1632=1200

100

1200×r×4

⟹r=9%

Now if rate is increased by 1% then r=(9+1)%=10%then amount will be,

A=P+

100

P×r×t

⟹A=1200

100

1200×10×4

⟹A=Rs.1680

Answer 2

Answer:

Let P(n):2

n

>n

When n=1,2

1

>1.Hence P(1) is true.

Assume that P(k) is true for any positive integer k,i.e.,

2

k

>k

we shall now prove that P(k+1) is true whenever P(k) is true.

Multiplying both sides of (1) by 2, we get

2.2

k

>2k

i.e., 2

k+1

>2k

k+k>k+1

∴2

k+1

>k+1