\(B=\dfrac{1}{99\cdot97}-\dfrac{1}{97\cdot95}-\dfrac{1}{95\cdot93}-...-\dfrac{1}{3\cdot1}\)
\(B=-\left(\dfrac{1}{3\cdot1}+\dfrac{1}{5\cdot3}+...+\dfrac{1}{97\cdot99}\right)\)
\(2B=-\left(\dfrac{2}{3\cdot1}+\dfrac{2}{5\cdot3}+...+\dfrac{2}{99\cdot97}\right)\)
\(2B=-\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(2B=-\left(1-\dfrac{1}{99}\right)\)
\(2B=-\dfrac{98}{99}\)
\(B=-\dfrac{98}{198}\)
`#3107`
`B = 1/(99*97) - 1/(97*95) - 1/(95*93) - ... - 1/(5*3) - 1/(3*1)`
`= 1/(99*97) - (1/(1*3) + 1/(3*5) + ... + 1/(95*97) )`
`= 1/2*(2/(97*99) ) - 1/2*(2/(1*3) + 2/(3*5) + ... + 2/(95*97) )`
`= 1/2*(1/97 - 1/99) - 1/2*(1 - 1/3 + 1/3 - 1/5 + ... + 1/95 - 1/97)`
`= 1/2*(1/97 - 1/99) - 1/2*(1 - 1/97)`
`= 1/2*(1/97 - 1/99 - 1 + 1/97)`
`= 1/2*(-9502/9603)`
`= -4751/9603`