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Convert the recurrings decimal 3.5overse...

Convert the recurrings decimal `3.5overset(•)2` into a rational number.

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The correct Answer is:
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`3.5overset(•)2=3.52222...=3.5+(0.02+0.002+0.0002+...oo)`
`=(35)/(10)+(0.02)/(1-0.1)" (sum of infinite terms)"`
`=(35)/(10)+(0.02)/(0.9)=(35)/(10)+(2)/(90)`
`=(315+2)/(90)=(317)/(90).`
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NAGEEN PRAKASHAN ENGLISH-SEQUENCE AND SERIES-Miscellaneous Exercise
  1. Convert the recurrings decimal 3.5overset(•)2 into a rational number.

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  2. 32. Show that the sum of (m+n)^(th) and (m-n)^(th) terms of an A.P. is...

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  3. The sum of three numbers in A.P. is 27, and their product is 504, find...

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  4. Let the sum of n, 2n, 3n terms of an A.P. be S1,S2and S3, respectively...

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  5. Find the sum of all numbers between 200 and 400 which are divisible...

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  6. Find the sum of integers from 1 to 100 that are divisible by 2 or 5...

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  7. Find the sum of all two digit numbers which when divided by 4, yiel...

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  8. If f is a function satisfying f(x+y)=f(x)f(y)for all x ,y in Xsuch t...

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  9. The sum of some terms of G. P. is 315 whose first term and the comm...

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  10. The first term of a G.P. is 1. The sum of the third and fifth terms is...

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  11. The sum of three numbers m GP is 56. If we subtract 1.7,21 from the...

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  12. A G.P. consists of an even number of terms. If the sum of all the t...

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  13. The sum of the first four terms of an A.P. is 56. The sum of the la...

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  14. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0),then show that...

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  15. LetS be the sum, P the product, and R the sum of reciprocals of n term...

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  16. The p^(t h),q^(t h)and r^(t h)terms of an A.P. are a, b, c, respectiv...

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  17. If a (1/b+1/c),b(1/c+1/a),c(1/a+1/b)are in A.P., prove that a, b, c a...

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  18. If a, b, c, d are in G.P., prove that (a^n+b^n),(b^n+c^n),(c^n+a^n)ar...

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  19. If a and b are the roots of x^2-3x+p=0and c, d are roots of x^2-12 x+...

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  20. The ratio of the A.M. and G.M. of two positive numbers a and b, is m ...

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  21. If a ,\ b ,\ c are in A.P. b ,\ c ,\ d are in G.P. and 1/c ,1/d ,1/e a...

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