e to the Power of Infinity

The constant e is fundamental in describing continuous growth or decay, and it forms the base of all natural logarithms. Since e > 1, raising it to larger and larger exponents causes the values to tend to infinity.

Mathematically, lim x→∞   e^x= ∞

Here, x increases without limit, so ex also increases without limit and diverges to infinity.

For example:
e¹ ≈ 2.718
e¹⁰ ≈ 22026.465
e¹⁰⁰ ≈ 2.688 × 10⁴³

As the exponent increases to infinity, the value also becomes infinitely larger.

• Infinity: It is the concept that describes something without a limit.

• Divergence: This term is used for a sequence or function that increases infinitely instead of reaching a finite value.

• Limit: The value a function/sequence approaches as the input approaches infinity or a particular point is known as the limit.