幫我呀!(+5分)

[(1+100)*100]/2

=(101*100)/2

=10100/2

=5050

2007-03-19 21:35:12 補充：
在計算這種題目時,常會用到一條公式,[(首項+末項)*項數]/2套用至這條題目中1+2+3+...+100,其中,首項是1,末項是100,而項數是100.因此有,1+2+3+4+5+....+98+99+100=[(1+100)*100]/2=5050

=5050

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84+85+86+87+88+89+90+91+92+93+94+95+96+97+98+99+100=?

=1+100*100/2

=5050

hope can help u~!!

<(100+1)x100>/2
<101x100>/2
10100/2
5050

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84+85+86+87+88+89+90+91+92+93+94+95+96+97+98+99+100=?
=5050

[(1+100)×100]÷2
=5050

1+100=2+99=3+98......
=101x50
=5050
^^ easy la~

1+2+3+4+5+6+7+8+9+10 +11+12+13+14+15+16+1 7+18+19+20+21+22+23+ 24+25+26+27+28+29+30 +31+32+33+34+35+36+3 7+38+39+40+41+42+43+ 44+45+46+47+48+49+50 +51+52+53+54+55+56+5 7+58+59+60+61+62+63+ 64+65+66+67+68+69+70 +71+72+73+74+75+76+7 7+78+79+80+81+82+83+ 84+85+86+87+88+89+90 +91+92+93+94+95+96+9 7+98+99+100=?
a = 1
d = 1
n = 100
S(n)
= (n/2)[2a + (n - 1)d]
= (100/2)[2(1) + (100 - 1)(1)]
= 50(101)
= 5050
? = 5050

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84+85+86+87+88+89+90+91+92+93+94+95+96+97+98+99+100
=101x50
=5050

50X3+100X50
=5000+150=5150