Question

Let an=(0.1)^n for all n belongs to N and €=0.00002.find the N such that aN+1,aN+2,... belongs to (-€,€)

Answer 1

yes .

matk me as brainliest

Answer 2

Given :    aₙ = (0.1)ⁿ  for all n belongs to N and €=0.00002.

aN+1,aN+2,... belongs to (-€,€)

To Find :  N

Solution:

€=0.00002

=> € = 2 x 10⁻⁵

- € =  -2 x 10⁻⁵

  € = 2 x 10⁻⁵

-2 x 10⁻⁵  <  (0.1)ⁿ  < 2 x 10⁻⁵

(0.1)ⁿ > 0  hence  only need to check

(0.1)ⁿ < 2 x 10⁻⁵

0.1³ = 1 x 10⁻⁴ >  2 x 10⁻⁵

0.1⁴ = 1 x 10⁻⁵  < 2 x 10⁻⁵

0.1⁵  = 1 x 10⁻⁶  <  2 x 10⁻⁵  

0.1⁶  = 1 x 10⁻⁷  <  2 x 10⁻⁵

=> n ≥  4

n = N+ 1, N + 2 ,....................

Hence  N = 3

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