Find the sum of the series .4+.44+.444 upto n terms
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let s(n)=0.4+0.44+0.444+....
= 4(0.1+0.11+0.111+...)
= (4/9)(0.9+0.99+0.999+...)
= (4/9)((1-0.1)+(1-0.01)+(1-0.001)+.....)
= (4/9) (1+1+1.... -(0.1+0.01+0.001)+.....)
= (4/9)(n - (1-(0.1)ⁿ)/9)
= 4(0.1+0.11+0.111+...)
= (4/9)(0.9+0.99+0.999+...)
= (4/9)((1-0.1)+(1-0.01)+(1-0.001)+.....)
= (4/9) (1+1+1.... -(0.1+0.01+0.001)+.....)
= (4/9)(n - (1-(0.1)ⁿ)/9)
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