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If an infinite G.P. has 2nd term x and i...

If an infinite G.P. has 2nd term x and its sum is 4, then prove that `xin(-8,1]-{0}`

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To solve the problem, we need to analyze the given information about the infinite geometric progression (G.P.) and derive the necessary conditions for the second term \( x \) based on the sum of the series. ### Step-by-step Solution: 1. **Identify the Terms of the G.P.**: Let the first term of the infinite G.P. be \( a \) and the common ratio be \( r \). The second term can be expressed as: \[ \text{Second term} = ar = x ...
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Statement 1: If an infinite G.P. has 2nd term x and its sum is 4, then x belongs to (-8,1)dot Statement 2: Sum of an infinite G.P. is finite if for its common ratio r ,0<|r|<1.

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Knowledge Check

  • If an infinite G.P. has the first term a and the sum 5, then which one of the following is correct?

    A
    A. `alt-10`
    B
    B. `-10ltalt0`
    C
    C. `0ltalt10`
    D
    D. `agt10`

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    A
    2
    B
    `(5)/(2)`
    C
    `(7)/(2)`
    D
    `(3)/(2)`

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