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Evaluate the value of the infinite sum sin⁻¹ ((1)/(√(2)))+sin⁻¹ ((√(2)-1)/(√(6)))+sin⁻¹ ((√(3)-√(2))/(√(12)))+⋯+sin⁻¹ ((√(n)-√(n-1))/(√(n(n+1))))+⋯.

1. π/8
2. π/4
3. π/2
4. π

Correct answer: π/2

Solution

The infinite sum converges to (C0)/(2) because each term in the series represents the inverse sine of a value that approaches the limit of 1 as n increases, leading to the cumulative angle approaching (C0)/(2).

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