Question

A small block slides without friction down the inclined plane starting from rest .let Sn be tge distance travelled from t=n-1 to n=t .then Sn/Sn+1 is

Answer 1

Answer:

Explanation:

For distance $S_n$ travelled from $(n-1)$ to n,

$S_n= 0 [n-n-1)]+\large\frac{1}{2} $$a[n^2-(n-1)^2]$

$S_n = \large\frac{1}{2}$$a [n^2-(n^2+1-2n)]$

$S_n= \large\frac{a}{2}$$(2n-1)$

Again , $ S_{n+1}= \large\frac{1}{2}$$a[(n+1)^2-n^2]$

$\qquad= \large\frac{a}{2} $$[2n+1]$

$\large\frac{S_n}{S_{n+1}}=\large\frac{\frac {a}{2} (2n-1)}{\frac{a}{2} (2n+1)}$

$\qquad= \large\frac{2n-1}{2n+1}$