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b) S=32+34+...+3998+31000
S=(32+34)+[(36+38+310)+(312+314+316)....+(3996+3998+31000)]
S= 90+ [36. 91+312.6+...+3996. 91]
Vì 91 chia hết cho 7 nên: 36. 91+312.6+...+3996. 91 cũng chia hết cho 9
Mà 90 chia 7 dư 6 nên suy ra S cũng chia 7 dư 6
Vậy S chia 7 dư 6
Nếu đúng k cho mk nha
Lời giải:
$S=3^2+3^4+3^6+...+3^{998}+3^{1000}$
$3^2S=3^4+3^6+3^8+...+3^{1000}+3^{1002}$
$\Rightarrow 3^2S-S=3^{1002}-3^2$
$\Rightarrow 8S=3^{1002}-9$
$\Rightarrow S=\frac{3^{1002}-9}{8}$
b.
$S=3^2+3^4+(3^6+3^8+3^{10})+(3^{12}+3^{14}+3^{16})+...+(3^{996}+3^{998}+3^{1000})$
$=90+3^6(1+3^2+3^4)+3^{12}(1+3^2+3^4)+...+3^{996}(1+3^2+3^4)$
$=90+(1+3^2+3^4)(3^6+3^{12}+...+3^{996})$
$=90+91(3^6+3^{12}+...+3^{996})$
$=6+ 12.7+7.13(3^6+3^{12}+...+3^{996})$ chia $7$ dư $6$
a)S=3^0+3^2+3^4+...+3^2000+3^2002
=>3^2S=3^2(3^0+3^2+3^4+...+3^2000+3^2002)
=>9S=3^2+3^4+3^6+...+3^2002+3^2004
=>9S-S=(3^2+3^4+3^6+...+3^2004)-(3^0+3^2+3^4+...+3^2000+3^2002)
=>8S=3^2004-3^0=3^2004-1
=>S=(3^2004-1)/8
b) S=3^0+3^2+3^4+...+3^2000+3^2004
=>S=(3^0+3^2+3^4)+(3^6+3^8+3^10)+...+(3^1998+3^2000+3^2002)
=>S=(1+3^2+3^4)+3^6(1+3^2+3^4)+...+3^1998(1+3^2+3^4)
=>S=91+3^6.91+...+3^1998.91
=>S=91(1+3^6+...+3^1998)
=>S=7.13.(1+3^6+...+3^1998
=>S chia hết cho 7
b)Ta có:S=(30+32+34)+...(31996+31998+32000+32002)
S=91+...+31996.(1+32+34)
S=91+...+31996.91
S=91.(1+...+31996)
Vì 91chia hết cho 7 nên S chia hết cho 7
a) 9.S = 34+ 36+.....+ 31000+ 31002
9.S - S = (34+ 36+.....+ 31000+ 31002) - ( 32+ 34+.....+ 3998+ 31000)
8.S = 31002 - 32
S =31002 - 32 / 8
a) \(S=3^2+3^4+...+3^{998}+3^{1000}\)
\(\Rightarrow3^2.S=3^2.3^2+3^2.3^4+...+3^2.3^{998}+3^2.3^{1000}\)
\(9S=3^4+3^6+...+3^{1000}+3^{1002}\)
\(\Rightarrow8S=9S-S=\left(3^4+3^6+...+3^{1000}+3^{1002}\right)-\left(3^2+3^4+...+3^{998}+3^{1000}\right)\)
\(=3^{1002}-3^2\)
\(=3^{1002}-9\)
\(\Rightarrow S=\dfrac{3^{1002}-9}{8}\)