# Could you please prove the following equation from Arithmetic Progressions?

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If #a_1# , ... , #a_n# are in AP where, #a_i > 0# for all #i# , then show that

#1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_2)+sqrt(a_3))+....+1/(sqrt(a_n-1)+sqrt(a_n))= (n-1)/(sqrt(a_1)+sqrt(a_n))# .

If

##### 1 Answer

Feb 25, 2018

See below.

#### Explanation:

If the sequence

and then

but