if $$3+14(3+P)+142(3+2P)+143(3+3P)+$$....∞$$=8then$$ the value of P is

Correct option is 3is a perfect square of a natural number

Questions

$i f 3 + \frac{1}{4} (3 + P) + \frac{1}{4^{2}} (3 + 2 P) + \frac{1}{4^{3}} (3 + 3 P) + .... \infty = 8$ then the value of P is

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detailed solution

Correct option is C

The given series can be written as 31+14+142+......+P41+2.14+3.142+.....=8Use the sum of infinte GP and infinite AGP formulae ⇒3×11−14+P411−14+141−142=8 ⇒3×43+P443+14×169=84+P49=8P=9

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if 3+14(3+P)+142(3+2P)+143(3+3P)+....∞=8then the value of P is

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$i f 3 + \frac{1}{4} (3 + P) + \frac{1}{4^{2}} (3 + 2 P) + \frac{1}{4^{3}} (3 + 3 P) + .... \infty = 8$ then the value of P is