Question

The positive integer just greater than (1 + 0.0001)¹⁰⁰⁰⁰ is(a) 4(b) 5(c) 2(d) 3

Answer 1

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Answer 2

Option d - The positive integer just greater than (1 + 0.0001)¹⁰⁰⁰⁰ is 3.

Step-by-step explanation:

To find : The positive integer just greater than (1 + 0.0001)¹⁰⁰⁰⁰ is ?

Solution :

The positive integer just greater than (1 + 0.0001)¹⁰⁰⁰⁰

Writing it as,

(1 + 0.0001)^{10000}=(1+\frac{1}{10000})^{10000}

The given form is in form of

$(1+\frac{1}{n})^{n}=1+n\times\frac{1}{n}+\frac{n(n-1)}{2}\times\frac{1}{n^2}+...$

$(1+\frac{1}{n})^{n}=1+1+(\frac{1}{2!})(1-\frac{1}{n})+...$

$(1+\frac{1}{n})^{n}=2+k$

where, k will be less than 1,

So, 3 is the next positive integer.

Therefore, the positive integer just greater than (1 + 0.0001)¹⁰⁰⁰⁰ is 3.

Hence, option (d) is correct.

#Learn more

Q4. Number of non-negative integral values of x satisfying the inequality 2 x 2 - x + 1 - 1 x + 1 - 2 x - 1 x 3 + 1 ≥ 0 is

(A) 0 (B) 1 (C) 2 (D) 3

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