Question

Please help me to solve this

Answer 1

(c) 2n-1/2n+1

$\bf\huge\underline{\underline{ Given :- }}$

• Distance = $\bf S_{n}$

• time , t¹ = n - 1

• time , t² = n

$\bf\huge\underline{\underline{ To \: Find:- }}$

• $\bf \frac{S_{n} }{S_{n}+1}$

$\bf\huge\underline{\underline{ Answer :- }}$

• t¹ = n - 1

• t² = n

• ∆t = t² - t¹

• $\red{\implies}$ ∆t = n - n - 1

$\rule{10cm}{0.0005cm}$

• $\boxed{\bf\red{ s = ut + \frac{1}{2} at²}}$

• $\bf S_{n} = 0[n-n-1] + \frac{1}{2} a[n² - (n-1)²]$

• $\bf S_{n} = \frac{a}{2}(n² - (n² + 1 - 2n )$

• $\bf S_{n} = \frac{a}{2}(n² - n² - 1 + 2n )$

• $\bf S_{n} = \frac{a}{2} ( 2n -1 )$

$\rule{10cm}{0.0005cm}$

• $\bf S_{n+1} = 0[n+1 -n] + \frac{1}{2} a[(n+ 1)²-n²]$

• $\bf S_{n+1} = \frac{1}{2} a[n²+ 1+2n-n²]$

• $\bf S_{n+1} = \frac{a}{2} (2n+ 1)$

$\rule{10cm}{0.0005cm}$

• $\bf \frac{S_{n} }{S_{n}+1}$

• $\bf\red{\implies} \frac{\frac{a}{2}(2n-1)}{\frac{a}{2}(2n+1)}$

• $\bf\red{\implies} \frac{2n-1}{2n+1}$

$\rule{10cm}{0.05cm}$