-|[[p_(1)],[[-(1)/(3)]+[-(1)/(3)-(1)/(del^(0))]]+[-(1)/(3)-(2)/(10)0]+cdots+[-(1)/(3)-(99)/(100)]

[[-(1)/(3)]+[-(1)/(3)-(1)/(100)]+[-(1)/(3)-(2)/(100)]+...+[-(1)/(3)-(99)/(100)] is equal to (where [.] denotes greatest integer function)

[-(1)/(3)]+[-(1)/(3)-(1)/(100)]+[-(1)/(3)-(2)/(100)]+….+[-(1)/(3)-(99)/(100)] is equal to (where [.] denotes greatest integer function)

[(1)/(1*2)+(1)/(2*3)+(1)/(3*4)+....+(1)/(99*100)] =?

[(1)/(1xx2)+(1)/(2xx3)+(1)/(3xx4)+,+(1)/(99xx100)]=

The following steps are involved in finding the value of 10 (1)/(3) xx 9(2)/(3) by using an appropriate indentity . Arrange them in sequential order . (A) (10)^(2) - ((1)/(3))^(2) = 100 - (1)/(9) (B) 10(1)/(3) xx 9(2)/(3) = (10 + (1)/(3)) (10 - (1)/(3)) (C) (10 + (1)/(3)) (10 - (1)/(3)) = (10)^(2) - ((1)/(3))^(2) [because (a + b) (a -b) = (a^(2) - b^(2))] (D) 100 - (1)/(9) = 99 + 1 - (1)/(9) = 99(8)/(9)

(1.99)^(3)-3(1.99)+5~~…

Evaluate ((0.6)^(0)-(0.1)^(-1))/(((3)/(8))^(-1)((3)/(2))^(3)+((-1)/(3))^(-1))