Q 31 If a1,a2, ,an are in AP where, ai 0 for all i, then - Maths - Arithmetic Progressions

Question

Q   31   I f   a 1 , a 2 , , a n   a r e  
i n   A P   w h e r e ,   a i > 0   f o r
  a l l   i ,   t h e n   s h o w   t h a
t 1 a 1 + a 2 + 1 a 2 + a 3 + + 1 a n - 1 + a n   =   1 a
1 + a n

Shruti Tyagi · Accepted Answer

Dear student,

The correct question to prove is 1a1+a2+1a2+a3+
+1an-1+an=n-1a1+an
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Regards

Q 31 . I f a 1 , a 2 , . . . . . , a n a r e i n A P w h e r e , a i > 0 f o r a l l i , t h e n s h o w t h a t 1 a 1 + a 2 + 1 a 2 + a 3 + . . . . + 1 a n - 1 + a n = 1 a 1 + a n

$Q 31 . I f a_{1}, a_{2}, . . . . ., a_{n} a r e i n A P w h e r e, a_{i} > 0 f o r a l l i, t h e n s h o w t h a t \frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + . . . . + \frac{1}{\sqrt{a_{n - 1}} + \sqrt{a_{n}}} = \frac{1}{\sqrt{a_{1}} + \sqrt{a_{n}}}$