Etymology
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thank (v.)

Old English þancian, þoncian "to give thanks, thank, to recompense, to reward," from Proto-Germanic *thankōjanan (source also of Old Saxon thancon, Old Norse þakka, Danish takke, Old Frisian thankia, Old High German danchon, Middle Dutch, Dutch, German danken "to thank"), from *thankoz "thought; gratitude," from PIE root *tong- "to think, feel."

It is related phonetically to think as song is to sing; for sense evolution, compare Old High German minna "loving memory," originally "memory." Also compare related Old English noun þanc, þonc, originally "thought," but also "good thoughts, gratitude." In ironical use, "to blame," from 1550s. To thank (someone) for nothing is recorded from 1703. Related: Thanked; thanking.

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thank you 
polite formula used in acknowledging a favor, c. 1400, short for I thank you (see thank). As a noun, from 1792.
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thankless (adj.)
"likely to not be rewarded with thanks," 1540s, from thank + -less. Related: Thanklessly; thanklessness.
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thankful (adj.)
Old English þancful "satisfied, grateful," also "thoughtful, ingenious, clever;" see thank + -ful. Related: Thankfully; thankfulness. Thankfully in the sense "thankful to say" is attested by 1966, but deplored by purists (compare hopefully).
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thanks (n.)

mid-13c., plural of thank (n.), from Old English þanc, þonc in its secondary sense "grateful thought, gratitude," from Proto-Germanic *thanka-, from the same root as thank (v.). In prehistoric times the Germanic noun seems to have expanded from "a thinking of, a remembering" to also mean "remember fondly, think of with gratitude." Compare Old Saxon thank, Old Frisian thank, Old Norse þökk, Dutch dank, German Dank. The Old English noun chiefly meant "thought, reflection, sentiment; mind, will, purpose," also "grace, mercy, pardon; pleasure, satisfaction."

As short for I give you thanks from 1580s; often with extensions, such as thanks a lot (1908). Spelling thanx attested by 1907.

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think (v.)

Old English þencan "imagine, conceive in the mind; consider, meditate, remember; intend, wish, desire" (past tense þohte, past participle geþoht), probably originally "cause to appear to oneself," from Proto-Germanic *thankjan (source also of Old Frisian thinka, Old Saxon thenkian, Old High German denchen, German denken, Old Norse þekkja, Gothic þagkjan).

Old English þencan is the causative form of the distinct Old English verb þyncan "to seem, to appear" (past tense þuhte, past participle geþuht), from Proto-Germanic *thunkjan (source also of German dünken, däuchte). Both are from PIE *tong- "to think, feel" which also is the root of thought and thank.

The two Old English words converged in Middle English and þyncan "to seem" was absorbed, except for its preservation in archaic methinks "it seems to me."

As a noun, think, "act of prolonged thinking," is attested by 1834. The figurative thinking cap is attested from 1839.

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kew 
1939, as a clipped form of thank you.
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TGIF 
also T.G.I.F., by 1946, slang abbreviation of "Thank God (or "goodness"), it's Friday" (end of the work week).
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grace (v.)
c. 1200, "to thank," from Old French graciier "thank, give thanks to; praise," from grace "mercy, favor, thanks, virtue" (see grace (n.)). Meaning "to show favor" (mid-15c.) led to that of "to lend or add grace to something" (1580s, as in grace us with your presence), which is the root of the musical sense in grace notes (1650s). Related: Graced; gracing.
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pickthank (n.)

also pick-thank, c. 1500, "an officious fellow who does what he is not asked to do for the sake of gaining favor, a parasite or toady," from phrase pick thanks "procure consideration or favor by servile or underhanded means" (early 15c.); see pick (v.) + thanks.

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