SOLUTION: 1/log2a+1/log4a+1/log8a+......upto n term

Question 991818: 1/log2a+1/log4a+1/log8a+......upto n term
Answer by ikleyn(52915)   (Show Source): You can put this solution on YOUR website!
.
+ + + . . . . . upto n term
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Notice that

= .

It is the consequence of the "base change formula" for logarithms (see any Algebra textbook or the lesson Change of Base Formula for logarithms in this site).

Therefore, we can re-write the formula in the form

+ + + . . . + = + + + . . . +

Next, notice that    = ,    = , . . . ,    = .

Thus you have, actually, the sum

+ + + . . . + = .(1 + 2 + 3 + . . . +n),

which is equal to   ..

Answer. The sum is equal to . = ..

Thank you for submitting so exciting problem.

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