If b is the first term of an infinite G.P.

Question

If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

Accepted Answer

Sum of infinite G.P, S = $$b \over {1-r}$$ where $$\left| r \right| < 1$$ $$ \Rightarrow $$ 5 = $$b \over {1-r}$$ $$ \Rightarrow $$ 1 - r = $$b \over 5$$ $$ \Rightarrow $$ b = 5(1 - r) as $$\left| r \right| < 1$$ $$ \therefore $$ -1 < r < 1 $$ \Rightarrow $$ 1 > -r > -1 $$ \Rightarrow $$ 2 > 1-r > 0 $$ \Rightarrow $$ 10 > 5(1-r) > 0 $$ \Rightarrow $$ 10 > b > 0 $$ \therefore $$ interval of b = (0, 10)

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