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Q:
Simple inequality $\sum_{i=1}^{n} 2^i – \sum_{i=1}^{n} i \leq 2^n $
Is there a simple inequality for which $\forall n\in \mathbb{N}:$
$$\sum_{i=1}^{n} 2^i – \sum_{i=1}^{n} i \leq 2^n $$
?
Thank you in advance!
A:
$$\sum_{i=1}^n (2^i-i) = \sum_{i=1}^n 2^i – \sum_{i=1}^n i = 2^n-n+2^n =2^n$$
A. Technical Field
The present invention relates to a liquid ejecting apparatus, a liquid ejecting system, an ejecting method, and a non-transitory computer readable medium.
B. Background Art
A liquid ejecting apparatus, such as an ink jet type printer, includes a liquid ejecting head (ejecting head) having an ejecting opening configured to discharge ink (a liquid). In the liquid ejecting apparatus, the ejecting opening of the liquid ejecting head is caused to eject ink supplied to the ejecting opening, thereby forming an image on a recording medium, for example.
In such a liquid ejecting apparatus, the ink contained in the ejecting opening of the liquid ejecting head is easily thickened due to evaporation, air bubbles, and the like. When the ink thickened is ejected from the ejecting opening, the image formed on the recording medium is poor, and the ink is also thickened inside the liquid ejecting apparatus.
Accordingly, the maintenance is periodically performed in the liquid ejecting apparatus, in which a cap is attached to the ejecting opening of the liquid ejecting head, and an ink supply opening of a supply tank communicating with the liquid ejecting head is allowed to communicate with the cap to expel the ink thickened in the liquid ejecting head. JP-A-2007-57511 is an example of related art.The present invention generally relates to a print head and a method of forming the print head and, more particularly, to a print head that is capable of effectively ejecting ink droplets in response to small and large amplitude signals and a method of forming the print head.
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