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The sum to infinity of the series (1) -1 + (1+2) -1 +(1+2+3) -1 + ... is?

The sum to infinity of the series (1)-1 + (1+2)-1 +(1+2+3)-1 + ... is?

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1 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

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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