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The sum to infinity of the series (1)-1 + (1+2)-1 +(1+2+3)-1 + ... is?
Hi Prajesh,
Again here will give you the method. Please do the workings.
Consider the "r"th term in the series
Tr = (1+2+3+....r)-1 = 2/{r(r+1) = 2*[ 1/r - 1/(r+1) ]
Now summation of this Tr from r=1 to r=∞,
Would be 2[1-1/2] + 2[1/2-1/3] + 2[1/3-1/4] +...........
Note that the negative term in one bracket gets cancelled with the positive term in the next bracket.
So the sum S = 2
[Ok, have worked it out fully :-)]
Hope that helps.
Best Regards,
Ashwin (IIT Madras).
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