Question

Find the sum of 10terms of the progression log2+log4+log8+log 16....

Answer 1

Answer

log2+log4+log8+log16+log32+log64+log128+log256+log512+log1024

The sum of 10 terms of the progression is 55log(2).

Step-by-step explanation:

The given progression is

\log 2+\log 4+\log 8+\log 16+...

We need to find the sum of 10 terms of the progression.

The given progression can be rewritten as

\log 2^1+\log 2^2+\log 2^3+\log 2^4+...

So, the sum of first 10 terms is

\log 2^1+\log 2^2+\log 2^3+\log 2^4+...+\log 2^{10}

Using the property of logarithm we get

1\log 2+2\log 2+3\log 2+4\log 2+...+10\log 2 [\because \log x^a=a\log x]

Taking log 2 common.

\log 2(1+2+3+4+5+6+7+8+9+10)

\log 2(55)

55\log 2

Therefore, the sum of 10 terms of the progression is 55log(2).

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