Solve 100+(10*(0.0425+0.0425^2+0.0425^2+0.0425^3+0.0425^4+{0.0425}^{5}+{0.0425}^6+{0.0425}^7+{0.0425}^8+{0.0425}^9))

$$100+(10 \times (0.0425+ { 0.0425 }^{ 2 } + { 0.0425 }^{ 2 } + { 0.0425 }^{ 3 } + { 0.0425 }^{ 4 } + { 0.0425 }^{ 5 } + { 0.0425 }^{ 6 } + { 0.0425 }^{ 7 } + { 0.0425 }^{ 8 } + { 0.0425 }^{ 9 } ))$$

Evaluate

$$100.46192672976481226092899322509765625$$

Solution Steps

Calculate 0.0425 to the power of 2 and get 0.00180625.

$$100+10\left(0.0425+0.00180625+0.0425^{2}+0.0425^{3}+0.0425^{4}+0.0425^{5}+0.0425^{6}+0.0425^{7}+0.0425^{8}+0.0425^{9}\right)$$

Add 0.0425 and 0.00180625 to get 0.04430625.

$$100+10\left(0.04430625+0.0425^{2}+0.0425^{3}+0.0425^{4}+0.0425^{5}+0.0425^{6}+0.0425^{7}+0.0425^{8}+0.0425^{9}\right)$$

Calculate 0.0425 to the power of 2 and get 0.00180625.

$$100+10\left(0.04430625+0.00180625+0.0425^{3}+0.0425^{4}+0.0425^{5}+0.0425^{6}+0.0425^{7}+0.0425^{8}+0.0425^{9}\right)$$

Add 0.04430625 and 0.00180625 to get 0.0461125.

$$100+10\left(0.0461125+0.0425^{3}+0.0425^{4}+0.0425^{5}+0.0425^{6}+0.0425^{7}+0.0425^{8}+0.0425^{9}\right)$$

Calculate 0.0425 to the power of 3 and get 0.000076765625.

$$100+10\left(0.0461125+0.000076765625+0.0425^{4}+0.0425^{5}+0.0425^{6}+0.0425^{7}+0.0425^{8}+0.0425^{9}\right)$$

Add 0.0461125 and 0.000076765625 to get 0.046189265625.

$$100+10\left(0.046189265625+0.0425^{4}+0.0425^{5}+0.0425^{6}+0.0425^{7}+0.0425^{8}+0.0425^{9}\right)$$

Calculate 0.0425 to the power of 4 and get 0.0000032625390625.

$$100+10\left(0.046189265625+0.0000032625390625+0.0425^{5}+0.0425^{6}+0.0425^{7}+0.0425^{8}+0.0425^{9}\right)$$

Add 0.046189265625 and 0.0000032625390625 to get 0.0461925281640625.

$$100+10\left(0.0461925281640625+0.0425^{5}+0.0425^{6}+0.0425^{7}+0.0425^{8}+0.0425^{9}\right)$$

Calculate 0.0425 to the power of 5 and get 0.00000013865791015625.

$$100+10\left(0.0461925281640625+0.00000013865791015625+0.0425^{6}+0.0425^{7}+0.0425^{8}+0.0425^{9}\right)$$

Add 0.0461925281640625 and 0.00000013865791015625 to get 0.04619266682197265625.

$$100+10\left(0.04619266682197265625+0.0425^{6}+0.0425^{7}+0.0425^{8}+0.0425^{9}\right)$$

Calculate 0.0425 to the power of 6 and get 0.000000005892961181640625.

$$100+10\left(0.04619266682197265625+0.000000005892961181640625+0.0425^{7}+0.0425^{8}+0.0425^{9}\right)$$

Add 0.04619266682197265625 and 0.000000005892961181640625 to get 0.046192672714933837890625.

$$100+10\left(0.046192672714933837890625+0.0425^{7}+0.0425^{8}+0.0425^{9}\right)$$

Calculate 0.0425 to the power of 7 and get 0.0000000002504508502197265625.

$$100+10\left(0.046192672714933837890625+0.0000000002504508502197265625+0.0425^{8}+0.0425^{9}\right)$$

Add 0.046192672714933837890625 and 0.0000000002504508502197265625 to get 0.0461926729653846881103515625.

$$100+10\left(0.0461926729653846881103515625+0.0425^{8}+0.0425^{9}\right)$$

Calculate 0.0425 to the power of 8 and get 0.00000000001064416113433837890625.

$$100+10\left(0.0461926729653846881103515625+0.00000000001064416113433837890625+0.0425^{9}\right)$$

Add 0.0461926729653846881103515625 and 0.00000000001064416113433837890625 to get 0.04619267297602884924468994140625.

$$100+10\left(0.04619267297602884924468994140625+0.0425^{9}\right)$$

Calculate 0.0425 to the power of 9 and get 0.000000000000452376848209381103515625.

$$100+10\left(0.04619267297602884924468994140625+0.000000000000452376848209381103515625\right)$$

Add 0.04619267297602884924468994140625 and 0.000000000000452376848209381103515625 to get 0.046192672976481226092899322509765625.

$$100+10\times 0.046192672976481226092899322509765625$$

Multiply 10 and 0.046192672976481226092899322509765625 to get 0.46192672976481226092899322509765625.

$$100+0.46192672976481226092899322509765625$$

Add 100 and 0.46192672976481226092899322509765625 to get 100.46192672976481226092899322509765625.

$$100.46192672976481226092899322509765625$$

Factor

$$\frac{47 \cdot 86413 \cdot 1130191 \cdot 573736711397}{2 ^ {35} \cdot 5 ^ {17}} = 100\frac{1.210913206474644 \times 10^{22}}{2.62144 \times 10^{22}} = 100.4619267297648$$