\(A = 1 + 2 + 4 + 8 + 16 + ... + 1024 + 2048\)
\(⇒ 2 A = 2 + 4 + 8 + 16 + 32 + ... + 2048 + 4096\)
\(⇒ 2 A − A = ( 2 + 4 + 8 + 16 + 32 + ... + 2048 + 4096 ) − ( 1 + 2 + 4 + 8 + 16 + ... + 1024 + 2048 )\)
\(⇒ A = 4096 − 1\)
\(⇒ A = 4095\)
\(A = 1 + 2 + 4 + 8 + 16 + ... . . + 1024 + 2048\)
\(2 A = 2 + 4 + 8 + 16 + 32 + ... . + 2048 + 4096\)
\(2 A − A = ( 2 + 4 + 8 + 16 + 32 + ... . + 2048 + 4096 ) − ( 1 + 2 + 4 + 8 + 16 + ... . . + 1024 + 2048 )\)
\(A = 4096 − 1\)
\(A = 4095\)
A=1+2+4+8+16+...+1024+2048
⇒2A=2+4+8+16+32+...+2048+4096
⇒2A−A=(2+4+8+16+32+...+2048+4096)
−(1+2+4+8+16+...+1024+2048)
⇒A=4096−1
⇒A=4095