Solve 2^{10}+2^{9}+2^{8}+2^7+2^6+2^4+2^2+1

$$2 ^ { 10 } + 2 ^ { 9 } + 2 ^ { 8 } + 2 ^ { 7 } + 2 ^ { 6 } + 2 ^ { 4 } + 2 ^ { 2 } + 1$$

Evaluate

$$2005$$

Solution Steps

Calculate 2 to the power of 10 and get 1024.

$$1024+2^{9}+2^{8}+2^{7}+2^{6}+2^{4}+2^{2}+1$$

Calculate 2 to the power of 9 and get 512.

$$1024+512+2^{8}+2^{7}+2^{6}+2^{4}+2^{2}+1$$

Add 1024 and 512 to get 1536.

$$1536+2^{8}+2^{7}+2^{6}+2^{4}+2^{2}+1$$

Calculate 2 to the power of 8 and get 256.

$$1536+256+2^{7}+2^{6}+2^{4}+2^{2}+1$$

Add 1536 and 256 to get 1792.

$$1792+2^{7}+2^{6}+2^{4}+2^{2}+1$$

Calculate 2 to the power of 7 and get 128.

$$1792+128+2^{6}+2^{4}+2^{2}+1$$

Add 1792 and 128 to get 1920.

$$1920+2^{6}+2^{4}+2^{2}+1$$

Calculate 2 to the power of 6 and get 64.

$$1920+64+2^{4}+2^{2}+1$$

Add 1920 and 64 to get 1984.

$$1984+2^{4}+2^{2}+1$$

Calculate 2 to the power of 4 and get 16.

$$1984+16+2^{2}+1$$

Add 1984 and 16 to get 2000.

$$2000+2^{2}+1$$

Calculate 2 to the power of 2 and get 4.

$$2000+4+1$$

Add 2000 and 4 to get 2004.

$$2004+1$$

Add 2004 and 1 to get 2005.

$$2005$$

Factor

$$5\times 401$$