Let Sk-1-2-3-kk- IfS12-S22-S192-A4- then the value of A is

S_k=k(k+1)2k=k+12 S_1^2+S_2^2+⋯+S_19^2 =14(2^2+3^2+4^2+ ⋯ +20^2) =14(1^2+2^2+3^2+4^2 + ⋯ + 20^2 1) =14[20(21)(41)6 1] =28694 ∴ A= 2869 ...

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Sigma n2

Let Sk=1+2+3+...

Question

Let $S_{k} = \frac{1 + 2 + 3 + \dots + k}{k} .$ If
$S_{1}^{2} + S_{2}^{2} + \dots + S_{19}^{2} = \frac{A}{4},$ then the value of $A$ is

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S_{k} = \frac{1 + 2 + 3 + \dots + k}{k} .

S_{1}^{2} + S_{2}^{2} + \dots + S_{19}^{2} = \frac{A}{4},

A

S_{k} = \frac{1 + 2 + 3 + \dots + k}{k} .

S_{1}^{2} + S_{2}^{2} + + S_{10}^{2} = \frac{5}{12} A

A

S_{k} = \frac{1 + 2 + 3 + \dots + k}{k}

k \in N .

S_{1}^{2} + S_{2}^{2} + \dots + S_{19}^{2} = \frac{A}{4},

A

S_{k} = \frac{1 + 2 + 3 + . . . . + k}{k} .

S_{1}^{2} + S_{2}^{2} + . . . + S_{10}^{2} = \frac{5}{12} A

A

a = 4^{1 / 401} - 1

n \geq 2,

b_{n} =^{n} C_{1} +^{n} C_{2} \cdot a +^{n} C_{3} \cdot a^{2} + \dots +^{n} C_{n} \cdot a^{n - 1} .

b_{2006} - b_{2005}

4^{k},

k \in N,

k

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