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[ahohen_77]

I got a question on sequences and series from the cambridge textbook:
10c) Find the sum of the first 300 terms of:

1/1+1/2+2/2+1/3+2/3+3/3+1/4+2/4+3/4+4/4.....


thanks

 

[CM_Tutor]

(1 / 1) + (1 / 2) + (2 / 2) + (1 / 3) + (2 / 3) + (3 / 3) + (1 / 4) + (2 / 4) + (3 / 4) + (4 / 4) + ...
= (1 / 1) + [(1 / 2) + (2 / 2)] + [(1 / 3) + (2 / 3) + (3 / 3)] + [(1 / 4) + (2 / 4) + (3 / 4) + (4 / 4)] + ...
= (1 / 1) + [(1 + 2) / 2] + [(1 + 2 + 3) / 3] + [(1 + 2 + 3 + 4) / 4] + ... + [(1 + 2 + 3 + ... + n) / n] + ...

Each term now has an AP on the numerator, so can be summed. The terms are made by 1, 2, 3, 4, ... terms of the original series. Now, consider the value of 1 + 2 + 3 + ... + 24.

 

[ahohen_77]

Thanks! U rule!