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"If "y=x+x^(2)+x^(3)+...oo and |x|lt1, "...

`"If "y=x+x^(2)+x^(3)+...oo and |x|lt1, "then prove that "x=(y)/(1+y).`

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The correct Answer is:
N/a
`y=x+x^(2)+x^(3)+...oo`
`rArr" "y=(x)/(1-x)`
`rArr" "y-xy=x`
`rArr" "y=x+xy`
`rArr" "y=x(1+y)`
`rArr" "x=(y)/(1+y).`
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NAGEEN PRAKASHAN-SEQUENCE AND SERIES-Miscellaneous Exercise
  1. "If "y=x+x^(2)+x^(3)+...oo and |x|lt1, "then prove that "x=(y)/(1+y).

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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. If the sum of three numbers in A.P., is 24 and their product is 440...

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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 N s...

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

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

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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 ter...

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

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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 tha...

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  15. if S is the sum , P the product and R the sum of reciprocals of n term...

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  16. If pth,qth and rth terms of an A.P. are a, b, c respectively, then sho...

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

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

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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/eare in A....

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