Question

Solve. Log10+log100+log1000+.... Log10^n. How to solve this? Don't use progressions.

Answer 1

First log10= 1
log100=log10^2=2log10 = 2.
log10^n = n log10= n.

Now, Log10+log100+log1000+.... Log10^n

The above reduces to

= 1+2+3+......... n.

This is like the sum of first n natural numbers.

We know that Sum of first n natural numbers is n(n+1)/2.

Log10+log100+log1000+.... Log10^n = n(n+1)/2

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hope helped! ^^