What is (sqrt(n+1)-sqrt(n))^2 ?

The solution to (sqrt(n+1)-sqrt(n))^2 is 2n-2sqrt(n)sqrt(n+1)+1

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simplify (sqrt(n+1)-sqrt(n))^2

simplify

(n + 1 - n)^{2}

2 n - 2 n n + 1 + 1

Solution steps

(n + 1 - n)^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(n + 1 - n)^{2} = (n + 1)^{2} - 2 n + 1 n + (n)^{2}

= (n + 1)^{2} - 2 n + 1 n + (n)^{2}

Simplify

(n + 1)^{2} - 2 n + 1 n + (n)^{2} : 2 n - 2 n n + 1 + 1

= 2 n - 2 n n + 1 + 1

\frac{3}{( 3 x + 2 ) ^{5}} + e^{- \frac{x}{3}} - 2 x^{3} + cos (5 x)

(2 csc (x) - 1) (csc (x) + 1)

(- 3, 5) y (7, - 3)

\frac{2}{2 π + 8} + \frac{16 π ^{3}}{( 2 π + 8 ) ^{2}}

\frac{n ^{2} ( n + 1 ) ^{2}}{4}

What is (sqrt(n+1)-sqrt(n))^2 ?
The solution to (sqrt(n+1)-sqrt(n))^2 is 2n-2sqrt(n)sqrt(n+1)+1