What is n^{0.1}+(n-1)*0.2+(n-2)*0.3+(n-3)*0.4 ?

The solution to n^{0.1}+(n-1)*0.2+(n-2)*0.3+(n-3)*0.4 is n^{0.1}+0.9n-2

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simplify n^{0.1}+(n-1)0.2+(n-2)0.3+(n-3)*0.4

simplify

n^{0.1} + (n - 1) \cdot 0.2 + (n - 2) \cdot 0.3 + (n - 3) \cdot 0.4

n^{0.1} + 0.9 n - 2

Solution steps

n^{0.1} + (n - 1) \cdot 0.2 + (n - 2) \cdot 0.3 + (n - 3) \cdot 0.4

= n^{0.1} + 0.2 (n - 1) + 0.3 (n - 2) + 0.4 (n - 3)

Expand

0.2 (n - 1) : 0.2 n - 0.2

= n^{0.1} + 0.2 n - 0.2 + 0.3 (n - 2) + 0.4 (n - 3)

Expand

0.3 (n - 2) : 0.3 n - 0.6

= n^{0.1} + 0.2 n - 0.2 + 0.3 n - 0.6 + 0.4 (n - 3)

Expand

0.4 (n - 3) : 0.4 n - 1.2

= n^{0.1} + 0.2 n - 0.2 + 0.3 n - 0.6 + 0.4 n - 1.2

Group like terms

= n^{0.1} + 0.2 n + 0.3 n + 0.4 n - 0.2 - 0.6 - 1.2

Add similar elements:

0.2 n + 0.3 n + 0.4 n = 0.9 n

= n^{0.1} + 0.9 n - 0.2 - 0.6 - 1.2

Subtract the numbers:

- 0.2 - 0.6 - 1.2 = - 2

= n^{0.1} + 0.9 n - 2

(x^{2} - 2 x + 3) \cdot (x - 4)

2 y^{3} - 5 y^{2} - 19 y + 42

27 (m + 2 n)^{3} - (m - 6 n)^{3}

(a - 5 b)^{2} - 16 b^{2}

2 x^{3} + 54 y^{3} - 4 x - 12 y

What is n^{0.1}+(n-1)*0.2+(n-2)*0.3+(n-3)*0.4 ?
The solution to n^{0.1}+(n-1)*0.2+(n-2)*0.3+(n-3)*0.4 is n^{0.1}+0.9n-2