Solve 1/20(1+2(1.0049+1.0198+1.0440+1.0770+1.1180+1.1661+1.2206+1.2806+1.3453+1.4142))

$$\frac{ 1 }{ 20 } (1+2(1.0049+1.0198+1.0440+1.0770+1.1180+1.1661+1.2206+1.2806+1.3453+1.4142))$$

Evaluate

$$1.21905$$

Solution Steps

Add 1.0049 and 1.0198 to get 2.0247.

$$\frac{1}{20}\left(1+2\left(2.0247+1.044+1.077+1.118+1.1661+1.2206+1.2806+1.3453+1.4142\right)\right)$$

Add 2.0247 and 1.044 to get 3.0687.

$$\frac{1}{20}\left(1+2\left(3.0687+1.077+1.118+1.1661+1.2206+1.2806+1.3453+1.4142\right)\right)$$

Add 3.0687 and 1.077 to get 4.1457.

$$\frac{1}{20}\left(1+2\left(4.1457+1.118+1.1661+1.2206+1.2806+1.3453+1.4142\right)\right)$$

Add 4.1457 and 1.118 to get 5.2637.

$$\frac{1}{20}\left(1+2\left(5.2637+1.1661+1.2206+1.2806+1.3453+1.4142\right)\right)$$

Add 5.2637 and 1.1661 to get 6.4298.

$$\frac{1}{20}\left(1+2\left(6.4298+1.2206+1.2806+1.3453+1.4142\right)\right)$$

Add 6.4298 and 1.2206 to get 7.6504.

$$\frac{1}{20}\left(1+2\left(7.6504+1.2806+1.3453+1.4142\right)\right)$$

Add 7.6504 and 1.2806 to get 8.931.

$$\frac{1}{20}\left(1+2\left(8.931+1.3453+1.4142\right)\right)$$

Add 8.931 and 1.3453 to get 10.2763.

$$\frac{1}{20}\left(1+2\left(10.2763+1.4142\right)\right)$$

Add 10.2763 and 1.4142 to get 11.6905.

$$\frac{1}{20}\left(1+2\times 11.6905\right)$$

Multiply 2 and 11.6905 to get 23.381.

$$\frac{1}{20}\left(1+23.381\right)$$

Add 1 and 23.381 to get 24.381.

$$\frac{1}{20}\times 24.381$$

Convert decimal number 24.381 to fraction \frac{24381}{1000}.

$$\frac{1}{20}\times \frac{24381}{1000}$$

Multiply \frac{1}{20} times \frac{24381}{1000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 24381}{20\times 1000}$$

Do the multiplications in the fraction \frac{1\times 24381}{20\times 1000}.

$$\frac{24381}{20000}$$

Factor

$$\frac{7 \cdot 43 \cdot 3 ^ {4}}{2 ^ {5} \cdot 5 ^ {4}} = 1\frac{4381}{20000} = 1.21905$$