Prove that -1-n-n-1-n-1-1-where n is positive integer-

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Arithmetic Progression

Prove that ∑1...

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Prove that ∑1/\sqrt n+\sqrt{n+1}=\sqrt{n+1}-1,where n is positive integer.

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\sum_{k = 1}^{n - 1} (n - k) c o s \frac{2 k π}{n} = - \frac{n}{2}

n \geq 3

Prove that only one of the number n-1, n+1 or n+5 is divisible by 3, where n is any positive integer. Explain

C_{0} + \frac{C_{1}}{2} + \frac{C_{2}}{3} + . . . . . . . . . . + \frac{C_{n}}{n + 1} = \frac{2^{n + 1} - 1}{n + 1}

n

n (n + 1) (n + 2)

n

| I m (z^{n}) | \leq n | I m (z) | {| z |}^{n - 1}

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