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The sum of 0.2+0.22+0.222+. . . . To n t...

The sum of 0.2+0.22+0.222+. . . . To n terms is equal to

A

`((2)/(9))-((2)/(81))(1-10^(-n))`

B

`n-((1)/(9))(1-10^(-n))`

C

`((2)/(9))[n-((1)/(9))(1-10^(-n))]`

D

`((2)/(9))`

Text Solution

Verified by Experts

The correct Answer is:
C
`S_(n)=0.2+0.22+0.022+ . . .` upto n terms
`=2[0.1+0.11+0.111+` upto n terms]
`=(2)/(9)[0.9+0.99+0.999+ . . ."upto n terms"] `
`=(2)/(9)[(1-0.1)+(1-(0.1)^(2))`
`+(1-(0.1)^(3))+. . ."upto n terms"]`
`=(2)/(9)[n-((0.1)+(0.1)^(2)+(0.1)^(3)"+. . . untp n terms")]`
`=(2)/(9)[n-(0.1)([1-(0.1)^(n)])/(1-0.1)]`
`=(2)/(9)[n-(1)/(9)[1-10^(-n)]]`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 04-PAPER 2 (MATHMATICS)
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  5. If A=[(cosx,sinx),(sinx,-cosx)] and A("adj "A)=lamda[(1,0),(0,1)], the...

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  6. int(0)^(pi//2)(cosx)/((1+sinx)(2+sinx))dx is equal to

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  7. If f(y)=e^y,g(y)=y,y>0, and F(t)=int0^t f(t-y)g(y) dy, then

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  8. The solution of the differential equation (dy)/(dx)=(4x+y+1)^(2), is

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  9. If xsin((y)/(x))dy=[ysin((y)/(x))-x]dx and y(1)=(pi)/(2), then the val...

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  10. Find the differential equation of system of cocentric circles with cen...

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  12. Angles A, B, C of a deltaABC are in AP and b : c = sqrt3 : sqrt2, th...

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  13. IF alpha,beta are the roots of the equation 6x^(2)-5x+1=0, then the va...

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  14. If one of the lines of m y^2+(1-m^2)x y-m x^2=0 is a bisector of the a...

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  15. intsqrt(1-cosx)dx=?

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  17. The derivative of sinx^(3) w.r.t. cosx^(3) is

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  18. If f(x)=|x|^(3), then f'(0) equals

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