A = 2 + 2^2 + 2^3 + 2^4 + .... + 2^100

Question

thanhmai · Answer

Đ&aacute;p &aacute;n:          A    =    2    +      2      2      +      2      3      +    .    .    .    +      2        100         A=2+22+23+...+2100              =>2    A    =      2      2      +      2      3      +      2      4      +    .    .    .    +      2        101         2A=22+23+24+...+2101              =>2    A    &minus;    A    =    (      2      2      +      2      3      +    .    .    .    +      2        101        )    &minus;    (    2    +      2      2      +      2      3      +    .    .    .    +      2        100        )     2A&minus;A=(22+23+...+2101)&minus;(2+22+23+...+2100)              ->A    =      2        101        &minus;    2

thienthanh · Answer

$A=2+2^2+2^3+...+2^{100}$   $2A=2^2+2^3+2^4+...+2^{101}$   $2A-A=(2^2+2^3+...+2^{101})-(2+2^2+2^3+...+2^{100})$   $ to A=2^{101}-2$

A = 2 + 2^2 + 2^3 + 2^4 + …. + 2^100

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