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Q.The value of the infinite product

P = (7/9)×(26/28)×(63/65)×……×(n^3 – 1/n^3 + 1)…………………

Note by Shailendra Sahu 4 years, 1 month ago

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2/3 (from Putnam exam) Hint : Telescoping Sum – Zi Song Yeoh · 4 years, 1 month ago

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@Zi Song Yeoh – Pretty obvious actually – Zi Song Yeoh · 4 years, 1 month ago

plz tell me the solution – Shailendra Sahu · 4 years, 1 month ago

@Shailendra Sahu – Step 1: Factor the numerator and denominator.

Step 2: use (k+2)-1=k-1 and \((k + 1)^{2} - (k + 1) + 1 = k^{2} + k + 1\)

Step 3 : cancel and get 2/3 – Zi Song Yeoh · 4 years, 1 month ago

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TopNewest2/3 (from Putnam exam) Hint : Telescoping Sum – Zi Song Yeoh · 4 years, 1 month ago

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– Zi Song Yeoh · 4 years, 1 month ago

Pretty obvious actuallyLog in to reply

plz tell me the solution – Shailendra Sahu · 4 years, 1 month ago

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Step 2: use (k+2)-1=k-1 and \((k + 1)^{2} - (k + 1) + 1 = k^{2} + k + 1\)

Step 3 : cancel and get 2/3 – Zi Song Yeoh · 4 years, 1 month ago

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