If P 1 = 1 - w 2 + w 2 4 - w 3 8 + . . . . . . . . . . ∞ and P 2 = 1 - w 2 2 {where w is non-real root of the equation x 3 = 1 }, then P 1 P 2 is equal to

Question

If P 1 = 1 - w 2 + w 2 4 - w 3 8 + . . . . . . . . . . ∞ and P 2 = 1 - w 2 2 {where w is non-real root of the equation x 3 = 1 }, then P 1 P 2 is equal to,

MARKS App · Accepted Answer

P 1 = 1 1 + w 2 ∵ s u m o f i n f i n i t e G . P a + a α + a α 2 . . . = a 1 - α H e r e , α ∈ - 1,1 = 2 2 + w + 2 1 + 1 + w = 2 1 - w 2 ∵ 1 + w + w 2 = 0 Now, P 1 P 2 = 2 1 - w 2 × 1 - w 2 2 = 1

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