Home
Class 12
MATHS
If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo...

If `x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n dz=c+c/(r^2)+c/(r^4)+oo,` prove that `(x y)/z=(a b)/c`

Text Solution

Verified by Experts

We have,
`x=a/(1-1/r)=ar/(r-1)`
`y=b/(1-(-1/r))=(br)/(1+r)`
`z=c/(1-1/r^(2))`
`thereforexy=((ar)/(r-1))((br)/(r+1))=(abr^(2))/(r^(2)-1)`
`therefore (xy)/z=[((abr^(2))/(r^(2)-1))/((cr^(2))/(r^(2)-1))]=(ab)/c`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.62|1 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.63|1 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.60|1 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n d z=c+c/(r^2)+c/(r^4)+oo, prove that (x y)/z=(a b)/c

If, for real numbers a, b, c, r with |r| gt 1, x = a + (a)/(r ) + (a)/(r^(2)) +…, " " y = b - (b)/(r ) + (b)/(r^(2)) - (b)/(r^(3))+… and z = c + (c )/(r^(2)) + (c )/(r^(4)) +… , then show that xyc = abz.

Knowledge Check

  • If x = sum _(n =0) ^(oo) a^(n) , y = sum _(n=0) ^(oo) b ^(n), z= sum _(n=0)^(oo) c^(n) where a,b,c are in A.P. and |a| lt 1, |b| lt 1, |c| lt 1, thenx,y,z are in-

    A
    A.P.
    B
    H.P.
    C
    G.P.
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    If a/(q -r) = b/(r-p) = c/(p-q) , then prove that a + b + c = 0 =pa+ qb + rc .

    If x = a - (1)/(a), y = b - (1)/(b) and z = c - (1)/(c ) and a, b, c are in G.P., then show that (x+z)/(y) = r + (1)/(r ) , where r is the common ratio of the G.P.

    If a/(y+z) = b/(z + x) = c/(x+y) , then prove that (a(b-c))/(y^(2)-z^(2)) = (b(c-a))/(z^(2)-x^(2)) = (c(a-b))/(x^(2)-y^(2)) .

    Prove that (r_(1) -r)/(a) + (r_(2) -r)/(b) = (c)/(r_(3))

    If in Delta ABC, (a -b) (s-c) = (b -c) (s-a) , prove that r_(1), r_(2), r_(3) are in A.P.

    If (.^(n)P_(r-1))/(a)=(.^(n)P_(r))/(b)=(.^(n)P_(r+1))/(c) prove that , b^(2)=a(b+c)

    With usual notations, in triangle A B C ,acos(B-C)+bcos(C-A)+c"cos"(A-B) is equal to(a) (a b c)/R^2 (b) (a b c)/(4R^2) (c) (4a b c)/(R^2) (d) (a b c)/(2R^2)

    Home
    Profile