Question : The sum of the first 20 term of the series $\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+....$ is:
Option 1: 0.16
Option 2: 1.6
Option 3: 16
Option 4: 0.016
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Correct Answer: 0.16
Solution : Given: The sum of the first 20 terms of the series $\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+....$ So, $a_{1} =5$ and $a_{20} =5+(20-1)×1=24$ 20 th term $=\frac{1}{24×25}$ $=\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+.... + \frac{1}{24×25}$ $=\frac{1}{5}-\frac{1}{6} + \frac {1}{6} - \frac{1}{7}+\frac{1}{7}-\frac{1}{8}+..............+\frac{1}{24}-\frac{1}{25}$ $=\frac{1}{5}-\frac{1}{25}$ $=\frac{4}{25}$ $= 0.16$ Hence, the correct answer is 0.16.
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Question : The value of $15 \div 8-\frac{5}{4}$ of $\left(\frac{8}{3} \times \frac{9}{16}\right)+\left(\frac{9}{8} \times \frac{3}{4}\right)-\left(\frac{5}{32} \div \frac{5}{7}\right)+\frac{3}{8}$ is:
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Question : The value of $4 \div 12$ of $[3 \div 4$ of $\{(4-2) \times 6 \div 2\}]-2 \times 6 \div 8+3$ is:
Question : If $A=\frac{\sqrt{0.0004} \times \sqrt[3]{0.000008}}{\sqrt[4]{16000} \times \sqrt[3]{125000} \times \sqrt[4]{810}}$ and $B=\frac{\sqrt[3]{0.729} \times \sqrt[4]{0.0016}}{\sqrt{0.16}}$, then what is $A \times B$?
Question : Directions: By interchanging the given two signs which of the following equations will be correct? ÷ and +
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