Solve {l}{1+1.1+1.1^{2}+1.1^{3}}{+1.1^4+1.15^5}{+1.1^6+1.1^7}

$$\left. \begin{array} { l } { 1 + 1.1 + 1.1 ^ { 2 } + 1.1 ^ { 3 } } \\ { + 1.1 ^ { 4 } + 1.15 ^ { 5 } } \\ { + 1.1 ^ { 6 } + 1.1 ^ { 7 } } \end{array} \right.$$

Evaluate

$$11.8367352875$$

Solution Steps

Add 1 and 1.1 to get 2.1.

$$2.1+1.1^{2}+1.1^{3}+1.1^{4}+1.15^{5}+1.1^{6}+1.1^{7}$$

Calculate 1.1 to the power of 2 and get 1.21.

$$2.1+1.21+1.1^{3}+1.1^{4}+1.15^{5}+1.1^{6}+1.1^{7}$$

Add 2.1 and 1.21 to get 3.31.

$$3.31+1.1^{3}+1.1^{4}+1.15^{5}+1.1^{6}+1.1^{7}$$

Calculate 1.1 to the power of 3 and get 1.331.

$$3.31+1.331+1.1^{4}+1.15^{5}+1.1^{6}+1.1^{7}$$

Add 3.31 and 1.331 to get 4.641.

$$4.641+1.1^{4}+1.15^{5}+1.1^{6}+1.1^{7}$$

Calculate 1.1 to the power of 4 and get 1.4641.

$$4.641+1.4641+1.15^{5}+1.1^{6}+1.1^{7}$$

Add 4.641 and 1.4641 to get 6.1051.

$$6.1051+1.15^{5}+1.1^{6}+1.1^{7}$$

Calculate 1.15 to the power of 5 and get 2.0113571875.

$$6.1051+2.0113571875+1.1^{6}+1.1^{7}$$

Add 6.1051 and 2.0113571875 to get 8.1164571875.

$$8.1164571875+1.1^{6}+1.1^{7}$$

Calculate 1.1 to the power of 6 and get 1.771561.

$$8.1164571875+1.771561+1.1^{7}$$

Add 8.1164571875 and 1.771561 to get 9.8880181875.

$$9.8880181875+1.1^{7}$$

Calculate 1.1 to the power of 7 and get 1.9487171.

$$9.8880181875+1.9487171$$

Add 9.8880181875 and 1.9487171 to get 11.8367352875.

$$11.8367352875$$

Factor

$$\frac{3191 \cdot 296753}{2 ^ {10} \cdot 5 ^ {7}} = 11\frac{66938823}{80000000} = 11.8367352875$$