Question

Find the sum to n terms of the series 0.6+0.66+0.666+.....................

Answer 1

oh no sorry

Answer 2

S = 0.6 + 0.66 + 0.666 + 0.6666........
S - S = 0.6 + 0.06 + 0.006 + 0.0006 ......- a n.
an = 0.6 ( 10 ^-n - 1)/ (-0.9)
An = 2/3 ( 1 - 10^-n)
= 2/3 -2*10^-n/3
Now try using this general term.

Answer 3

We have
\[0.6+0.66+0.666+0.6666\]
Let's take 6 out from the series
\[6(0.1+0.11+0.111+0.1111+....\]
Now multiply and divide by 9
\[\frac{6}{9}(0.9+0.99+0.999+0.9999+....\]
\[\frac{6}{9}(1-0.1+1-0.01+1-0.001+1-0.0001+....\]
\[\frac{6}{9}(1-10^{-1}+1-10^{-2}+1-10^{-3}+...\]
all 1s add up to n
\[\frac{6}{9}(n-\frac{1}{10}\times \frac{1-(\frac{1}{10})^{n+1}}{1-\frac{1}{10}}\]

Answer 4

should you have

\[\frac{6}{9}\left(n-\frac{1}{10}\times \frac{1-(\frac{1}{10})^{n}}{1-\frac{1}{10}}\right)\]

Answer 5

I got the same result. And yes that's correct. Did you not understand my method? I ould explain it again.
ash2326 ---> Nice. :D