Solution of task "Teleskopiranje 6." by user "prv123"

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Oct. 3, 2023, 10:47 a.m. (2 years, 11 months)

User: prv123
Task: Teleskopiranje 6. (Hide problem text)

Neka je $n \in \mathbb{N}$ . Izračunaj sljedeću sumu: $1\cdot 1!+2\cdot 2!+\ldots +n\cdot n!$

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$2!-1!=1\cdot1!$

$3!-2!=2\cdot2!$

$4!-3!=3\cdot3!$

$\vdots$

$(n+1)!-n!=n\cdot n!$

Zbrajanjem dobivamo:

$(n+1)!-1=1\cdot1!+ 2\cdot2! +...+n\cdot n!$

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