Lưu ý : /= phần , ^ = mũ Tính : S = 1 + 1/2 + 1/2^2 + 1/2^4 +..+ 1/2^98 + 1/2^100 Cần gấp ạ cảm ơn

` S = 1 + 1/2 + 1/(2^2) + 1/(2^4) + ... + 1/(2^98)+1/(2^100) `

` => 4S = 4 + 1/(2^3) + 1/(2^4) + 1/(2^6) + ... + 1/(2^100) + 1/(2^102) `

` => 4S - S = ( 4 + 1/(2^3) + 1/(2^4) + 1/(2^6) + ... + 1/(2^100) + 1/(2^102) ) - (1 + 1/2 + 1/(2^2) + 1/(2^4) + ... + 1/(2^98)+1/(2^100) ) `

` => 3S = 3 + 1/(2^3) + 1/(2^102) - 1/2 = 3 + (-3)/8 + 1/(2^102) `

` => S=(3+(-3)/8+1/(2^102)):3 `

1-2-3-4+5-6-7-8+9 -10-11-12 + ............ + 97 -08-99-100

= - ( 1-2-3-4 ) + ( 5-6-7-8 ) + ( 9-10-11-12 ) + ( 97-98-99-100 ) 

= - 8 + ( 16 - ) + ( 24 - ) + ............. + ( - 200 )

= - 8. ( 1+2+3 + .......... + 25 )

= - 8. [( 25-1 ) : 1+ 1 . 26 : 2]

= - 8. 325

= - 2600

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