Question

a) 1/2 - (- 2/5) + 1/3 + 5/7 - (- 1/6) + (- 4/35) + 1/41

b) 1/ 100.99 - 1/ 99.98 - 1/ 98.97 - ..... - 1/ 3.2 - 1/ 2.1

Answer 1

b) \(\dfrac{1}{100.99}-\dfrac{1}{99.98}-\dfrac{1}{98.97}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)

\(=\dfrac{1}{100.99}-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{97.98}+\dfrac{1}{98.99}\right)\)

\(=\dfrac{1}{100.99}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{97}-\dfrac{1}{98}+\dfrac{1}{98}-\dfrac{1}{99}\right)\)

\(=\dfrac{1}{100.99}-\left(1-\dfrac{1}{99}\right)\)

\(=\dfrac{1}{100.99}-\dfrac{98}{99}=-\dfrac{9799}{9900}\)

Answer 2

1/2+2/5+1/3+5/7+1/6+(-4/35)+1/41

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