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In the book "Horizons_ exploring the universe-Cengage learning (2018)", p196, it states that

The nuclear reactions in a main-sequence star’s core fuse hydrogen to produce helium. Because main-sequence stellar cores are cooler than 100,000,000 K, the helium can’t overcome the Coulomb barrier to fuse in nuclear reactions, so it accumulates at the star’s center like ashes in a fireplace.

But if the temperature is not high enough to fuse helium, then how does the ending stage of a main sequence star is by burning its helium shell? Is fusing different from burning? If so, why doesn't a helium core star burning its core, even if it cannot reach the temperature about the Coulomb barrier?

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    $\begingroup$ Stars leave the main sequence before they start fusing helium. There's a good description for our Sun here. $\endgroup$
    – PM 2Ring
    Commented May 18, 2021 at 10:34

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The helium core becomes significantly denser and hotter after a star has left the main sequence.

Providing the overall mass of the star is greater than about 50% that of the Sun, the helium core will become hot enough to begin fusion whilst the star is a red giant.

From there, the star will pass through phases of burning helium in its core, then hydrogen and helium in shells around an inert core of carbon and oxygen.

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