How do you determine if a_n=1-1.1+1.11-1.111+1.1111-... converge and find the sums when they exist?

1 Answer
Apr 27, 2017

1.01010101...

Explanation:

a_n = 1 -1.1 + 1.11 - 1.111 + 1.1111 - ...

a_n = 1 + (-1.1 + 1.11) +(- 1.111 + 1.1111) +( - ...

a_n = 1 + (0.01) +(0.0001) +( - ...

we can say that it squence is geometric progression where
a_1 = 1, common ratio, r = 0.01/1 =0.0001/0.01 = 1/100

sum of infinity, s_oo = a_1/(1-r)

S_oo= 1/(1 - 1/100) = 1/(99/100) = 100/99 = 1.01010101...