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Q.The value of the infi nite product

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

Note by Shailendra Sahu
4 years, 6 months ago

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2/3 (from Putnam exam) Hint : Telescoping Sum

Zi Song Yeoh - 4 years, 6 months ago

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Pretty obvious actually

Zi Song Yeoh - 4 years, 6 months ago

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plz tell me the solution

Shailendra Sahu - 4 years, 6 months ago

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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, 6 months ago

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