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1-1/2+1/3-1/4+1/5........ sum to infinity

1-1/2+1/3-1/4+1/5........  sum to infinity

Grade:11

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
7 years ago

re arrange terms,

1 + 1/3 -1/2 +1/5 + 1/7 - 1/4 + 1/9 + 1/11 - 1/6 + 1/13 + 1/15 -1/8 .................=

[1 -1/2 + 1/3 - 1/4 +1/5 - 1/6 + 1/7 -1/8] + [1/9 + 1/11 + 1/13 + 1/15.......................]
odd numbers give (1/2) ln 2 in the limit.

So ln 2 + ln2 / 2 = 3/2 ln 2.

shr mohammad
b.tech, iit delhi

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