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Question
If a = 1 + b + b2 + b3 + ... to ∞, then write b in terms of a.
Solution
\[\text{ Here, a = 1, b, b^2 , b^3 , . . . \infty form an infinite G . P } . \]
\[ \]
\[ \therefore S_\infty = a = 1 + b + b^2 + b^3 + . . . \infty = \frac{1}{1 - b}\]
\[ \Rightarrow a = \frac{1}{1 - b}\]
\[ \Rightarrow 1 - b = \frac{1}{a} \]
\[ \Rightarrow b = 1 - \frac{1}{a}\]
\[ \therefore b = \frac{a - 1}{a}\]
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