perplexus.info :: Just Math : Given the terms, find the Fraction Value

Given the terms, find the Fraction Value (Posted on 2024-05-10)

Given that:

    n
S_n= Σ k/(k+1)!
   k=1

Find the value of:

1-S₂₀₂₂
--------
1-S₂₀₂₃

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Analytic solution

| Comment 2 of 3 |

S(t) = 1 - 1/(t+1)!

1 - S(t) = 1/(t+1)!

1 - S(t+1) = 1/(t+2)!

(1-S(t))/(1-S(t+1)) = t+2

Let t = 2022

(1-S(2022))/(1-S(2023)) = t+2

= 2024

Posted by Larry on 2024-05-10 12:26:55

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