1 、1/1×2 +1/2×3 +1/3×4 +1/4×5+……1/2010×2011 2 、0.2¹

1个回答

  • 1-1/2+1/2-1/3+……+1/2010-1/2011=2010/2011

    0.2¹º×(-5)¹¹+1-(4/5)²=-5+1-16/25=5又9/25

    (1/2+1/3+···+1/2009)×(1+1/2+1/3+···+1/2008)-(1+1/2+1/3+···+1/2009)×(1/2+1/3+···+1/2008)=(1+1/2+1/3+···+1/2009)×(1+1/2+1/3+···+1/2008)-(1+1/2+1/3+···+1/2008)-(1+1/2+1/3+···+1/2009)×(1+1/2+1/3+···+1/2008)+(1+1/2+1/3+···+1/2009)=1/2009

    满足任意相邻三个数的和为同一个常数,

    a1=a4=a7=……=a100=-7

    a2=a5=a8=……=a98=-1

    a3=a6=a9=……=a99=9

    a1+a2+a3+•••+a99+a100=33*(9-1-7)+a1=33-7=26