The sum of the infinite G.P. a + a $r^{2}$ + a $r^{3}$ . . . . . . a is finite. Then,

r > 1

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r < 0

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r > 0

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-1 < r < 1

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Solution

The correct option is D
-1 < r < 1

For the sum to exist, a $r^{n}$ should approach zero as n becomes infinity. This is possible when |r|<1

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Similar questions

\frac{r_{1}}{r_{2}} - \frac{r_{2}}{r_{3}}

A B C

(\frac{r_{1}}{r_{2}} - \frac{r_{2}}{r_{3}})

r_{1}, r_{2}

r_{3}

If the sides fo a triangle are in A.P. as well as in G.P. Then the value of $\frac{r_{1}}{r_{2}} - \frac{r_{2}}{r_{3}}$

△ A B C

a < b < c

r

r_{1}, r_{2}, r_{3}

A, B, C

r < r_{1} < r_{2} < r_{3}

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{r_{1} r_{2} r_{3}}{r}

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