Question

the interval for which the series 1+(x-1)+(x-1)^2+.......∞ may be summed is

Answer 1

plss....tell without the use of limit

Answer 2

that series would be convergen if
-1 < r < 1

Answer 3

with r = a2/a1 = (x-1)/1 = x-1
so, -1 < x-1 < 1
add by 1 , we get
-1 + 1 < x-1+1 < 1+1
0 < x < 2

Answer 4

that interval makes the series can be summed

Answer 5

if the value of r lies between -1 and 1 then only it is possible to sum it up
is this a fix case for it

Answer 6

yes, that's the rule if given geometri series and so that it converges the ratio must be in that interval