(1/1*2) - (1/2*3) - (1/3*4) . . . - (1/49*50)

Find the values of

(1/1*2) - (1/2*3) - (1/3*4) . . . - (1/49*50).

-- James

The ans is 1/50

(1/2)-(1/6)-(1/12).......-(1/2450)
-1/2(-1+1/3+1/6......+1/1275)----taking the reciprocal
-2(-1+3+6+......1275)---then by using Arithmetic progression we can calculate it.

@ TigerElango
U need not complicate it so much.. [BTW i would be surprised if you arrive at the ans in your approach]
Here is a simpler approach
Split every term as follows
1/1.2 = 1/1 - 1/2
1/2.3 = 1/2 - 1/3
...
...
1/49.50 = 1/49 - 1/50

If you do so and then cancel out the terms.. you will see that only
1/50 remains.

sundar give a wounderful explanation.....

nice keep it up...

Sundar,
I really appreciate the way you solved this problem. The Perfect approach to attack this problem. Hats off to u man :)