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GATE > Learn GATE Coaching > What is the value of n terms of the series 4+44+444+............
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What is the value of n terms of the series 4+44+444+......... ?

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= 4/9(9+99+999+...n terms) = 4/9(10-1+100-1+1000-1+...n terms) = 4/9(10+100+1000+...n terms -n) = 4/9(10^n/9 -n)
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4/9(9+99+999+... n terms) 4/9(10-1+100-1+1000-1+...n terms) 4/9(10+100+1000+... n terms - n) 4/9((10^n-10)/9 -n)
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= 4 ( 1 + 11 + 444 + ...) = 4/9( 9 + 99 + 999 +..) = 4/9 (10 - 1 + 100 - 1 + 1000 -1 ......) say n terms = 4/9( 10+ 100+1000 ..... +10^n - n) = 4/9{ ((10^n - 10)/9) -n}
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