Question

The Largest Integer n for which n²⁰⁰<5³⁰⁰ is:​

Answer 1

*Answer:—

Greatest integer n

for which => n²⁰⁰<5³⁰⁰ helds

Let us assume an integer n = 2

i.e., 2²⁰⁰<5³⁰⁰

can be written as

→ [(2)²]¹⁰⁰ < 5¹⁰⁰

→ (4)¹⁰⁰ < 5¹⁰⁰ ....True

for n = 2 given condition holds true

Now,

Let, next integer n = 3

→ (3)²⁰⁰ < 5¹⁰⁰

→ (3²)¹⁰⁰ < 5¹⁰⁰

→ 9¹⁰⁰ < 5¹⁰⁰ ....False

for n = 3 , given condition does not satisfied

Hence,

greatest integer is n = 2 for which condition

n²⁰⁰ < 5¹⁰⁰ holds true.

Answer 2

answer:-

$n^{200} < 5 ^{300} \\ it \: is \: true$