Question

Pls solve...
Thanks!

Answer 1

Answer:

$\frac{n}{2}$

Step-by-step explanation:

$(1 - \frac{1}{n + 1} ) + (1 - \frac{2}{n + 1}) + .......(1 - \frac{n}{n + 1})$

• take LCM in each section

$( \frac{n}{n + 1} ) + ( \frac{n - 1}{n + 1}) + ........( \frac{1}{n + 1})$

• since the denominator is same we can combine them all as

$\frac{(n) + (n - 1) + (n - 2) + ......(1)}{n + 1}$

• If you observe the Nominator. It is the sum of first n terms. Which we know already and equal to
• $1 + 2 + 3 + .......... + n = \frac{(n)(n + 1)}{2}$

• Using above formula

we get:

$\frac{ \frac{(n)(n + 1)}{2} }{n + 1}$

• It can be simplified as

$\frac{n}{2}$

Let me know if you have any doubt in explaination :)

Answer 2

Answer:

n/2

Step-by-step explanation:

The final answer is (n/2).

Hope it helps!