sum of 0.4+0.44+0.444......upto n terms
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Hi ,
Let S = 0.4+0.44+0.444+...+ n terms
S = 4[ 0.1+0.11+0.111+...+ n terms ]
S = 4/9[ 0.9+0.99+0.999+..+n terms ]
= 4/9[(1-0.1)+(1-0.01)+...+ n terms ]
= 4/9 [(1+1+..nterms)-
(0.1+0.01+..nterms)]
= 4/9 { n + [(1/10)( 1 - 1/10ⁿ )/( 1- 1/10 ) ] }
= 4/9 { n + ( 1 - 1/10ⁿ ) /9 }
S = 4/81 [ 9n - 9 - 1/10ⁿ ]
I hope this helps you.
: )
Let S = 0.4+0.44+0.444+...+ n terms
S = 4[ 0.1+0.11+0.111+...+ n terms ]
S = 4/9[ 0.9+0.99+0.999+..+n terms ]
= 4/9[(1-0.1)+(1-0.01)+...+ n terms ]
= 4/9 [(1+1+..nterms)-
(0.1+0.01+..nterms)]
= 4/9 { n + [(1/10)( 1 - 1/10ⁿ )/( 1- 1/10 ) ] }
= 4/9 { n + ( 1 - 1/10ⁿ ) /9 }
S = 4/81 [ 9n - 9 - 1/10ⁿ ]
I hope this helps you.
: )
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