Question

if a1, a2....... an are in arithmetic progression were ai is greater than 0. For all i then( 1 /square root of a1 +square root of a2) +(1/square root of a2 +square root of a3)........... +1/square root of a(n-1)+square root of an<br /><br />​

Answer 1

Step-by-step explanation:

1/(√a1 + √a2) +1/(√a2 + √a3) +.....

rationalize every term i.e

1/(√a1 + √a2) *(√a1-√a2)/(√a1-√a2)

=(√a1-√a2)/a1-a2

similarly every term

now, it becomes

(√a1-√a2)/a1-a2 + (√a2-√a3)/a2-a3 +.....

a1-a2=a2-a3=......=-d(common difference)

sum it

-1/d[√a1-√a2+√a2-√a3+.....+√a(n-1) -√an]

=(√an-√a1)/d