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For the infinite series 1 + 4x + 7x² + 10x³ +..., if its sum is 35/16 and |x| < 1, then the value of x is

1. 19/7
2. 1/5
3. 1/4
4. None of these

Correct answer: 1/5

Solution

This arithmetic-geometric series sums to (1+2x)/(1-x)^2. Setting it equal to 35/16 gives x=1/5 or x=19/7; since |x|<1, x=1/5.

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