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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?

Grade:

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 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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