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Beliebt Rechnen >

sum from n=1 to infinity of (sin(1))^n

Lösung

n = 1 \sum \infty (sin (1))^{n}

Lösung

\frac{1}{1 - sin ( 1 )} - 1

+1

Dezimale

5.30799 \dots

Schritte zur Lösung

n = 1 \sum \infty (sin (1))^{n}

Vereinfache

= n = 1 \sum \infty sin^{n} (1)

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

= n = 0 \sum \infty sin^{n} (1) - sin^{0} (1)

n = 0 \sum \infty sin^{n} (1) = \frac{1}{1 - sin ( 1 )}

= \frac{1}{1 - sin ( 1 )} - sin^{0} (1)

Vereinfache

= \frac{1}{1 - sin ( 1 )} - 1

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