left(1-frac{1}{3}right)left(1-frac{1}{4}right | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given expression is $\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right) \ldots \left(1-\frac{1}{25}\right)$.
Simp

Vedclass · Accepted Answer

$\frac{2}{25}$

Vedclass · Answer

(A) The given expression is $\left(1-\frac{1}{3}ight)\left(1-\frac{1}{4}ight)\left(1-\frac{1}{5}ight) \ldots \left(1-\frac{1}{25}ight)$.
Simplifying each term:
$= \left(\frac{3-1}{3}ight) 	imes \left(\frac{4-1}{4}ight) 	imes \left(\frac{5-1}{5}ight) 	imes \ldots 	imes \left(\frac{25-1}{25}ight)$
$= \frac{2}{3} 	imes \frac{3}{4} 	imes \frac{4}{5} 	imes \ldots 	imes \frac{23}{24} 	imes \frac{24}{25}$
Observing the pattern,the numerator of each fraction cancels out the denominator of the preceding fraction.
$= \frac{2}{{3}} 	imes \frac{{3}}{{4}} 	imes \frac{{4}}{{5}} 	imes \ldots 	imes \frac{{24}}{25}$
$= \frac{2}{25}$

$\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right) \ldots \left(1-\frac{1}{25}\right)$ is equal to

Similar Questions

What approximate value will come in the place of the question mark $(?)$ in the following equation? (You are not expected to calculate the exact value.)
$7441 \div 34 \times 12 = ? \times 9 + 110$

$\sqrt[3]{-2197} \times \sqrt[3]{-125} + \sqrt[3]{\frac{27}{512}}$

The value of $\frac{1}{2} + \frac{1}{2 \cdot 3} + \frac{1}{2 \cdot 3 \cdot 4} + \frac{1}{2 \cdot 3 \cdot 4 \cdot 5}$ is correct to three places of decimal:

$\frac{? \div 12}{0.2 \times 3.6} = 2$

What value will come in place of the question mark (?) in the following question? (You are not expected to calculate the exact value)
$10^{3} \times 100^{3} + 999999999 = 10^{?} + 10^{?}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module