已知数列{bn}满足bn=(-1)^n n(n+1) Sn是前n项和
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已知数列{bn}满足bn=(-1)^n n(n+1) Sn是前n项和
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n = (-1)^n .n(n+1)
if n is even
b(n-1) +bn
= -(n-1)n + n(n+1)
= 2n
Sn = b1+b2+...+bn
= (b1+b2)+(b3+b4)+...+(b(n-1) +bn)
= 2 + 4+...+ 2n
= (n+1)n/2
if n is odd
b(n-2)+b(n-1)
= -(n-2)(n-1) + (n-1)n
=2(n-1)
Sn = b1+b2+...+bn
=(b1+b2)+(b3+b4)+...+(b(n-2) +b(n-1)) +bn
=[ 2 + 4+...+ 2(n-1) ] - n(n+1)
= n( n-1)/2 - n(n+1)
= (n/2) [ n-1 - 2(n+1) ]
=-n( n+3)/2
S20=(20+1)20/2 =210
S21=-21( 21+3)/2 =-252
if n is even
b(n-1) +bn
= -(n-1)n + n(n+1)
= 2n
Sn = b1+b2+...+bn
= (b1+b2)+(b3+b4)+...+(b(n-1) +bn)
= 2 + 4+...+ 2n
= (n+1)n/2
if n is odd
b(n-2)+b(n-1)
= -(n-2)(n-1) + (n-1)n
=2(n-1)
Sn = b1+b2+...+bn
=(b1+b2)+(b3+b4)+...+(b(n-2) +b(n-1)) +bn
=[ 2 + 4+...+ 2(n-1) ] - n(n+1)
= n( n-1)/2 - n(n+1)
= (n/2) [ n-1 - 2(n+1) ]
=-n( n+3)/2
S20=(20+1)20/2 =210
S21=-21( 21+3)/2 =-252
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