limit as n approaches infinity of \sum_{i=1}^n 2/n sin(2((2i)/n+2))

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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lim_{n→ ∞}(∑_i=1ⁿ2n sin(2(2in +2)))

Solution

−12 cos(8)+12 cos(4)

Decimal

−0.25407…

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lim_{n→ ∞}(∑_i=1ⁿ2n sin(2(2in +2)))

Limit of Sum definition

The definite integral is defined as: lim_{n→ ∞}(∑_i=1ⁿ(f(c_i)Δ x))=∫_a^bf(x)dx
Where Δx=b−an , and c_i=a+Δx⋅i

Apply the limit of sum formula: ∫₀²sin(2(x+2))dx

Solve ∫₀²sin(2(x+2))dx: −12 cos(8)+12 cos(4)

=−12 cos(8)+12 cos(4)

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

limit as n approaches infinity of \sum_{i=1}^n 2/n sin(2((2i)/n+2))

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