1-(1/2)+(1/3)-(1/4)+......+(1/99)-(1/100) how can this become {(1/51)+(1/52)+(1/53)+(1/54)+...+(1/99)+(1/100)

Question

i was unable to understand this solutuion of the first part of thee serries which has alternative "+ve" for odd terms And "-ve" for even terms but next step ahs all +ve terms but first 50 numbers vanish??????

Answer 1

i think that the question is incomplete....

are both series infinite?

Answer 2

It doesn't.

If you put those series into excel and work them out, there are no two equal sums. The infinite series 1+(1/-2)+(1/3)+(1/-4)+... tends to 0.693147.
The series (1/51)+(1/52)+..+(1/100) equals 0.688172179. Close but no cigar.

Since the first series converges but the second series is divergent, there is potentially just one place where they can equal each other.

Answer 3

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Answer 4

if ur series is upto infinity, then
1-1/2+1/3-1/4+1/5-1/6+...............
=(1+1/2+1/3+1/4+1/5+1/6+...............)-(2*1/2+2*1/4+2*1/6+.........)
=(1+1/2+1/3+1/4+1/5+1/6+.......)-(1+1/2+1/3+1/4+1/5+1/6+.........)
=0
but the series to which u r telling to convert has certain value.so i thing this is a wrong problem.