log42 - log82 + log16 2 -…. to ∞ is  Select the correct option.
A) e2	B) ln2+1	C) ln2-1	D) 1-ln2	E) None of these
Required sum = 1/2 - 1/3 +1/4 - … to ∞   Now, loge(1 + X) = X - X2/2 + X3/3 - …   Therefore, loge2 = 1-1/2 + 1/3 - … to ∞   =&gt;1/2 - 1/3 + 1/4 .. to ∞ = 1 - loge2 = 1- ln2.   ANSWER:1-ln2
<result>D</result>
log42 - log82 + log16 2 -…. to ∞ is