Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
`        H1 H2.......Hn are n  HM  between a and b where a  is not equal to b then the value of [H1+a/H1-a]+[Hn+b/Hn-b]`
one year ago

```							i) As given terms are in HP, let (1/a), (1/H1), (1/H2), ---- (1/Hn), (1/b) are in AP [Total there are (n+2) terms and 'n' means] ii) ==> (1/b) = (1/a) + (n + 1)d, where d is the common difference of AP Solving d = (a - b)/(ab(n + 1)} iii) ==> 1/H1 = 1/a + d = (b*n + a)/{ab(n + 1)} ==> H1 = ab(n + 1)/(b*n + a) ==> H1/a = (b*n + b)/(b*n + a) Applying compenendo & dividendo property of ratios and simplifying, [If a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d)], (H1 + a)/(H1 - a) = (2b*n + a + b)/(b - a) iv) In similar process, taking 1/Hn = (1/b) - d we get, (Hn + b)/(Hn - b) = (2a*n + a + b)/(a - b) = -(2a*n + a + b)/(b - a) v) So from the above, adding (iii) & (iv), [(H1 + a)/(H1 - a)] + [(Hn + b)/(Hn - b)] = (2b*n + a + b - 2a*n - a - b)/(b - a) = 2n(b - a)/(b - a) = 2n Thus it is proved that [(H1 + a)/(H1 - a)] + [(Hn + b)/(Hn - b)] = 2n
```
one year ago
Think You Can Provide A Better Answer ?

## Other Related Questions on IIT JEE Entrance Exam

View all Questions »  ### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 731 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions