log2+log4+log8+......ধারাটির প্রথম দশটি পদের সমষ্টি কত?

A    45 log2

B    55 log2

C    65 log2

D    75 log2 

Solution

Correct Answer: Option B

 

প্রথম দশ পদ পর্যন্ত

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

=log2+log22+log23+log24+log25+log26+log27+log28+log29+log210

= log2+ 2log2+ 3log2+ 4log2+ 5log2+ 6log2+7 log2+ 8log2+ 9log2+ 10log2

= (1+2+3+4+5+6+7+8+9+10) * log2

= 55 log2

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