Question

数列大题，第二，三问不会，我想只有高手中的高手才能解决吧O(∩_∩)O~

Answer 1

(1)
{b[n]}={2,5,8,11,8,5,2}
(2)
c[1]+c[2]...+c[24] = c[49]+c[48]+...+c[26]
S = (c[1]+...+c[24])+c[25]+...+c[49]
= 2( c[25]+...+c[49] ) - c[25]
= 2*(2^25 - 1) - 1
= 2^26 - 3
(3)
n>=51时,
d[n] = 2+3*(n-51)
n<=50时,
d[n] = d[101-n] = 2+3*(50-n) = 149-3*(n-1)
d1,d2,..,d50为以149为首项,公差为-3的等差数列

n<=50时,
S[n] = n/2*(a[1]+a[n]) = 149n-3n(n-1)/2
n>=51时,
S[n] = S[50] + (n-50)/2*(a[51]+a[n])
= (149*50-3*50*49/2) + (n-50)+3(n-50)(n-51)/2 自己整理去吧