`1(1)/(3)+3(2)/(3)=`

Find the sum of G.P. : 1-(1)/(3)+(1)/(3^(2))-(1)/(3^(3))+ . . . .. . . . . to n terms.

1+ ((1)/(3) + (1)/(3^2) ) + (( 1)/( 3^3) + (1)/( 3^4) + (1)/( 3^5) ) + .... sum of the terms in the n^( th) bracket=

Find the sum of the following series to infinity: 1-(1)/(3)+(1)/(3^(2))-(1)/(3^(3))+(1)/(3^(4))+oo

If A=[(2,-1),(-1,2)] , then show that A^(-1) =[((2)/(3),(1)/(3)),((1)/(3),(2)/(3))]

If x=1+(1)/(3)+(1)/(3^(2))+(1)/(3^(3))+.........oo , then (0.16)^(log_(2.5)x)

1+((1)/(3)+(1)/(3^(2)))+((1)/(3^(3))+(1)/(3^(4))+(1)/(3^(5)))+ sum of the terms in the n^(th) bracket =

evaluate lim_ (n rarr oo) [(1) / (3) + (1) / (3 ^ (2)) + (1) / (3 ^ (2)) + ......... + (1) / (3 ^ (n))]

lim_ (x rarr oo) {(1) / (3) + (1) / (3 ^ (2)) + (1) / (3 ^ (3)) + ...... (. 1) / (3 ^ (n))} =

lim_ (n rarr oo) ((1) / (3) + (1) / (3 ^ (2)) + (1) / (3 ^ (3)) ++ (1) / (3 ^ (n) ))