Geometric progression

Algebra Level 1

lim ⁡ m → ∞ ∑ n = 1 m 1 2 n = ? \displaystyle \lim_{m \to \infty} \sum_{n=1}^{m} \dfrac{1}{2^{n}} = \, ?


The answer is 1.

Sriram Radhakrishnan by Sriram Radhakrishnan , 22, India

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1 solution

Ossama Ismail
Apr 14, 2016

This summation can be expressed in binary system as 0.11111 … 1 = 1 0 . 11111\dots 1 = 1 as m → ∞ m \to \infty

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Or simply the summation is just a GP :)

Arulx Z - 5 years, 1 month ago

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