當(dāng)n=1時,a1=1
當(dāng)n=2時,a2=2,a3=a2+1+1=4
當(dāng)n=2k+1時(k屬于正整數(shù)),a(2k+2)-a(2k+1)=1+(-1)^(2k+1),a(2k+2)=a(2k+1)
當(dāng)n=2k+2時(k屬于正整數(shù)),a(2k+3)-a(2k+2)=1+(-1)^(2k+2),a(2k+3)=2+a(2k+2)
相加：
a(2k+2)+a(2k+3)=2+a(2k+1)+a(2k+2)
a(2k+3)=2+a(2k+1)
a(2k+3)=a3+2k=4+2k
即a(2k+1)=4+2(k-1)=2(k+1)
又a(2k+2)=a(2k+1)
所以a(2k+2)=a(2k+1)=2(k+1)
a(2k+2)+a(2k+1)=4(k+1)
所以
S(2k+2)=a1+a2+a3+a4+a5+a6+……+a(2k-1)+a(2k)+a(2k+1)+a(2k+2)
=(a1+a2)+[a3+a4]+[a5+a6]+……+[a(2k-1)+a(2k)]+[a(2k+1)+a(2k+2)]
=3+4(1+1)+4(2+1)+……+4k+4(k+1)
=3+8k+4k(k-1)/2
=3+k(2k+6)
所以當(dāng)k=49時
S100=3+49(2×49+6)
=3+49×104
=5099