Question

\(A=\frac{1}{1.2.3}-\frac{1}{2.3.4}-.....-\frac{1}{97.98.99}\)

Answer 1

\(A=\frac{1}{1.2.3}-\frac{1}{2.3.4}-........-\frac{1}{97.98.99}\)

\(2A=\frac{2}{1.2.3}-\frac{2}{2.3.4}-........-\frac{2}{97.98.99}\)

\(2A=-\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+....+\frac{2}{97.98.99}\right)\)

\(2A=-\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+......+\frac{1}{97.98}-\frac{1}{98.99}\right)\)

\(2A=-\left(\frac{1}{1.2}-\frac{1}{98.99}\right)\)

\(2A=-\frac{2425}{4851}\)

\(A=-\frac{2425}{4851}:2\)

\(A=-\frac{2425}{9702}\)

Answer 2

\(\frac{98}{99}\)

Answer 3

A= 1-1/2-1/3-1/2-1/3-1/4-....-1/97-1/98-1/99

A=1-1/99

A=99/99-1/99

A= 98/99

Answer 4

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