Question

B= 9/1.4 + 9/4.7 + ... + 9/97.100

Answer 1

\(B=\dfrac{9}{1\cdot4}+\dfrac{9}{4\cdot7}+...+\dfrac{9}{97\cdot100}\)

\(B=3\cdot\left(\dfrac{3}{1\cdot4}+\dfrac{3}{7\cdot10}+...+\dfrac{3}{97\cdot100}\right)\)

\(B=3\cdot\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)

\(B=3\cdot\left(1-\dfrac{1}{100}\right)\)

\(B=3\cdot\left(\dfrac{100}{100}-\dfrac{1}{100}\right)\)

\(B=3\cdot\dfrac{99}{100}\)

\(B=\dfrac{297}{100}\)