That's A.P

Algebra Level 2

The value of (1-1/n)+(1-2/n)+(1-3/n)+........... upto n terms is:

(n-1)/2 1 n(n+1)/2 0

1 solution

Sanjeet Raria
Nov 6, 2014

We see that for a fixed $n$ , each terms of the sequence is the difference of two AP. Hence our sequence is also an AP. Now $S_n=\frac{n}{2}(a+l)$

$a=$ first term = $(1-\frac{1}{n})$

$l=$ last term = $(1-\frac{n}{n})=0$

Putting all the value we get, $S_n=\frac{n}{2}(1-\frac{1}{n}+0)=\Large \frac{(n-1)}{2}$