In this
" 2log2 = 2 - 2/2 +2/3 -2/4 +2/5 -2/6...
= 2- 1 + 2/3 -1/2 +2/5 -1/3...
=1 -1/2 + 1/3 -1/4 .... "
You should divide both sides by 2
So You get log2=log2 which is obviously true
log(1+x)= x - xx/2 + xxx/3 - xxxx/4 .......
x=1, log 2 = 1 - 1/2 + 1/3 -1/4 ....
multiply both sides by 2, 2log2 = 2 - 2/2 +2/3 -2/4 +2/5 -2/6...
= 2- 1 + 2/3 -1/2 +2/5 -1/3...
=1 -1/2 + 1/3 -1/4 ....
2log2 = log 2
2=1
In this
" 2log2 = 2 - 2/2 +2/3 -2/4 +2/5 -2/6...
= 2- 1 + 2/3 -1/2 +2/5 -1/3...
=1 -1/2 + 1/3 -1/4 .... "
You should divide both sides by 2
So You get log2=log2 which is obviously true