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log2 + log4 + log16 + log256 + ... এই ধারার প্রথম দশটি পদের সমষ্টি কত?

A 210 log2

B 2log2

C (210 - 1)log2

D (29 - 1)log2

Solution

Correct Answer: Option C

log2 + log4 + log16 + log256 + ...
প্রথম 10টি পদ হবে,
log(2¹) + log(2²) + log(2⁴) + log(2⁸) + log(2¹⁶) + log(2³²) + log(2⁶⁴) + log(2¹²⁸) + log(2²⁵⁶) + log(2⁵¹²)
= = (1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512)log2
= (2¹⁰ - 1)log2

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