Given-the-equation-1000-2000-1-1-t-n-t-find-the-value-of-t-

Question Number 144049 by physicstutes last updated on 20/Jun/21

Given the equation 1000 = 2000 (\frac{1 - {(1 + t)}^{- n}}{t})

find the value of t .

Answered by Olaf_Thorendsen last updated on 21/Jun/21

1000 = 2000 (\frac{1 - {(1 + t)}^{- n}}{t})

\frac{1 - {(1 + t)}^{- n}}{t} = \frac{1}{2}

\frac{1}{1 + t} . \frac{1 - {(\frac{1}{1 + t})}^{n}}{1 - \frac{1}{1 + t}} = \frac{1}{2}

q (1 - q^{n}) = \frac{1}{2} (1 - q)

Let q = \frac{1}{1 + t}

q^{n + 1} - \frac{3}{2} q + \frac{1}{2} = 0