Login

Find the sum of the sequence 0.4, 0.44, 0.444……. up to n terms.

explaning each step

$Given 0.4 + 0.44 + 0.444 + ..... n terms = 4 (0.4 + 0.11 + 0.111....... n terms) multiply and divide by 9 we get = \frac{4}{9} (0.9 + 0.99 + 0.999....... + n terms) = \frac{4}{9} [(1 - 0.1) + (1 - (0.1)^{2}) + (1 - (0.1)^{3}) ...... n terms] = \frac{4}{9} [(1 + 1 + 1 + ..... n terms) - (0.1 + {0.1}^{2} + {0.1}^{3} ....... n terms)] = \frac{4}{9} [n - 0.1 (\frac{1 - (0.1)^{n}}{1 - 0.1})] = \frac{4}{9} [n - \frac{1 - (0.1)^{n}}{9}]$

23

View Full Answer

Copyright © 2024 Aakash EduTech Pvt. Ltd. All rights reserved.

Aakash EduTech Pvt. Ltd.

What are you looking for?