\(P=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{97.98}\\ P=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{97}-\dfrac{1}{98}\\ P=1-\dfrac{1}{98}\\ P=\dfrac{97}{98}\)
`@An`
\(P=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{97\cdot98}\)
\(P=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{97}+\dfrac{1}{97}-\dfrac{1}{98}\)
\(P=1-\dfrac{1}{98}\)
\(P=\dfrac{97}{98}\)
` P = 1/(1.2) + 1/(2.3)+...+1/(97.98) = (2-1)/(1.2)+(3-2)/(2.3)+...+(98-97)/(97.98) = 1/2-1/3+1/3-1/4+...+1/97-1/98=1/2-1/98=49/98-1/98=48/98 =24/49 `
