Question : The next term of the sequence $\left (1+\frac{1}{2} \right):\left (1+\frac{1}{2} \right) \left (1+\frac{1}{3} \right): \left (1+\frac{1}{2} \right)\left (1+\frac{1}{3} \right)\left (1+\frac{1}{4} \right): .........$ is:
Option 1: $3$
Option 2: $\left (1+\frac{1}{5} \right)$
Option 3: $5$
Option 4: $\left (1+\frac{1}{2} \right)\left (1+\frac{1}{5} \right)$
Correct Answer: $3$
Solution : Given sequence: $\left (1+\frac{1}{2} \right):\left (1+\frac{1}{2} \right) \left (1+\frac{1}{3} \right): \left (1+\frac{1}{2} \right )\left (1+\frac{1}{3} \right)\left (1+\frac{1}{4} \right): .........$ $T{_1}= 1+\frac{1}{2} = \frac{3}{2}$ $T{_2}= (1+\frac{1}{2})(1+\frac{1}{3}) = \frac{3}{2}\times \frac{4}{3}= 2$ $T{_3}= (1+\frac{1}{2})(1+\frac{1}{3})(1+\frac{1}{4}) = \frac{3}{2}\times \frac{4}{3}\times \frac{5}{4}= \frac{5}{2}$ $T{_4}= (1+\frac{1}{2})(1+\frac{1}{3})(1+\frac{1}{4})(1+\frac{1}{5}) = \frac{3}{2}\times \frac{4}{3}\times \frac{5}{4}\times \frac{6}{5}= 3$ Hence, the correct answer is $3$.
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Question : The value of $\left[1 \frac{2}{7} \times\left\{3 \frac{1}{2} \div\left(\frac{1}{2}-\frac{1}{7}\right)\right\}\right] \div\left(4 \frac{1}{5} \times 1 \frac{1}{2}\right)$ is:
Question : The value of $\left(5 \frac{1}{4} \div \frac{3}{7}\right.$ of $\left.\frac{1}{2}\right) \div\left(5 \frac{1}{9}-7 \frac{7}{8} \div 9 \frac{9}{20}\right) \times \frac{11}{21}+\left(2 \div 2\right.$ of $\left.\frac{1}{2}\right)$ is:
Question : Directions: Select the option related to the third term in the same way as the second term is related to the first term and the sixth term is related to the fifth term.
Question : The value of $1 \frac{2}{5}-\left[3 \frac{3}{4} \div\left\{1 \frac{1}{4} \div \frac{1}{2}\left(1 \frac{1}{2} \times 3 \frac{1}{3} \div 1 \frac{1}{3}\right)\right\}\right]$ is:
Question : The value of $\left(5 \div 2\right.$ of $\left.\frac{1}{2}\right)+\left(5 \frac{1}{4} \div \frac{3}{7}\right.$ of $\left.\frac{1}{2}\right) \div\left(5 \frac{1}{9}-7 \frac{7}{8} \div 9 \frac{9}{20}\right) \times \frac{11}{21}$ is:
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