which one is true for the mathematical expression 2 n + 2 n − 1 2 n + 1 − 2 n ?

which one is true for the mathematical expression 2 n + 2 n − 1 2 n + 1 − 2 n ? ?

Created: 1 year ago | Updated: 2 months ago | Created By:

Nihar Afrin

3/2

2/3

2 30

0 19

Institution: Bank Asia Ltd Exam: Bank Asia Ltd - Management Trainee Officer - 22.05.2015 ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To evaluate the expression \( \frac{2^n + 2^{n-1}}{2^{n+1} - 2^n} \), we can simplify it step by step.

First, we rewrite the numerator:
\[ 2^n + 2^{n-1} = 2^n + \frac{2^n}{2} = 2^n(1 + \frac{1}{2}) = 2^n \cdot \frac{3}{2}. \]

Now, let's simplify the denominator:
\[ 2^{n+1} - 2^n = 2^n \cdot 2 - 2^n = 2^n(2 - 1) = 2^n \cdot 1 = 2^n. \]

Now we can substitute back into the expression:
\[
\frac{2^n \cdot \frac{3}{2}}{2^n}.
\]

Since \(2^n\) is common in both numerator and denominator, it cancels out, leaving us with:
\[
\frac{3}{2}.
\]

Thus, the expression simplifies to \( \frac{3}{2} \), which corresponds to option A. Therefore, the correct answer to the question is \( \frac{3}{2} \).

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which one is true for the mathematical expression 2 n + 2 n − 1 2 n + 1 − 2 n ? ?

If 3 x − 3 x − 1 = 18 , t h e v a l u e o f x x i s :

2 30 + 2 30 + 2 30 + 2 30 = ?

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