设数列{an},{bn}是分别以d1,d2为公差的等差数列,a1=50,b51设数列{an},{bn}是分别以d1,d2为公差的等差数列,a1=50,b51=100.(1) 若ak=bk=0,且数列a1,a2,...,ak,bk+1,bk+2,...,b51的前n项和为Sn,若S51

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设数列{an},{bn}是分别以d1,d2为公差的等差数列,a1=50,b51设数列{an},{bn}是分别以d1,d2为公差的等差数列,a1=50,b51=100.(1)若ak=bk=0,且数列a1

设数列{an},{bn}是分别以d1,d2为公差的等差数列,a1=50,b51设数列{an},{bn}是分别以d1,d2为公差的等差数列,a1=50,b51=100.(1) 若ak=bk=0,且数列a1,a2,...,ak,bk+1,bk+2,...,b51的前n项和为Sn,若S51
设数列{an},{bn}是分别以d1,d2为公差的等差数列,a1=50,b51
设数列{an},{bn}是分别以d1,d2为公差的等差数列,a1=50,b51=100.(1) 若ak=bk=0,且数列a1,a2,...,ak,bk+1,bk+2,...,b51的前n项和为Sn,若S51=3Sk,求数列{an},{bn}通项公式.(2)在符合(1)的条件下,求数列{(-d1)^(bn/4)+26}的前n项和Tn

设数列{an},{bn}是分别以d1,d2为公差的等差数列,a1=50,b51设数列{an},{bn}是分别以d1,d2为公差的等差数列,a1=50,b51=100.(1) 若ak=bk=0,且数列a1,a2,...,ak,bk+1,bk+2,...,b51的前n项和为Sn,若S51
先将两个数列的一部分列排列如下:
a1,a2,a3,.,ak
bk,bk+1,.b51
S51=(a1+a2+.+ak)+(b[k+1]+b[k+2]+.+b51)
=(50+0)*k/2+(bk+b[k+1]+b[k+2]+.+b51) (因为bk=0,加入后对和的大小没影响)
=25k+(0+100)*(52-k)/2
=25k+2600-50k
=2600-25k
又因为S51=3Sk=3*(50+0)*k/2=75k
所以
75k=2600-25k
k=26
d1=(a26-a1)/25=(0-50)/25=-2
d2=(b51-b26)/25=(100-0)/25=4
b1=b26-25d2=0-25*4=-100
an=a1+(n-1)d1=50+(n-1)*(-2)=52-2n
bn=b1+(n-1)d2=-100+(n-1)*4=-104+4n
--------------------------------------------------------
设数列{cn}={(-d1)^(bn/4)+26}
cn=2^[(-104+4n)/4]+26
=2^(n-26)+26
=(2^n)/(2^26)+26
则Tn=c1+c2+.+cn
=[2/(2^26)+26]+[4/(2^26)+26]+[8/(2^26)+26]+.+[(2^n)/(2^26)+26]
=[2*(2^n-1)/(2-1)]/(2^26)+26n
=[2^(n+1)-2]/(2^26)+26n
=2^(n-25)-2^(-25)+26n

“数列a1,a2,...,ak,bk+1,bk+2,...,b51的前n项和为Sn”没看明白

数列a1,a2,...,ak,bk+1,bk+2,...,b51的前n项和为Sn,应该是a1,a2,...,ak,bk+1,bk+2,...,bn的和吧?若是则过程如下:
1)设通项an=a1+(n-1)d1=50+(n-1)d1, bn=b1+(n-1)d2
由于bk+1=bk+d2=d2故
Sn=(a1+.....+ak)+(bk+1+....+bn)
=ka...

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数列a1,a2,...,ak,bk+1,bk+2,...,b51的前n项和为Sn,应该是a1,a2,...,ak,bk+1,bk+2,...,bn的和吧?若是则过程如下:
1)设通项an=a1+(n-1)d1=50+(n-1)d1, bn=b1+(n-1)d2
由于bk+1=bk+d2=d2故
Sn=(a1+.....+ak)+(bk+1+....+bn)
=ka1+k(k-1)d1/2+(n-k)b(k+1)+(n-k)(n-k-1)d2/2
=50k+k(k-1)d1/2+(n-k)d2+(n-k)(n-k-1)d2/2
又 ak=bk=0, 即50+(k-1)d1=0 (1)
b1+(k-1)d2=0, (2)
b51=b1+50d2=100 (3)
s51=50*51+50*51d1/2+0++0
3sk=3*(a1+a2+.....+ak)=3ka1+3k(k-1)d1/2=150k+3k(k-1)d1/2
s51=3sk (4)
由(4)得,100k+k(k-1)d1=(51-k)d2+(51-k)(50-k)d2/2 (5)
由(3)-(2)得 100=(51-k)d2,代入(5)
100k+k(k-1)d1=100+50(50-k) (6),将(1)代入(6)
50k=100+50(50-k) ,解得k=26 代入(1)得d1=-2
代入(2)(3)解得d2=4,b1=-100
故an=50+(n-1)d1=-2n+52
bn=-100+(n-1)d2=4n-104
2)设cn=(-d1)^(bn/4)+26=2^(n-26)+26 ???这个26是在指数上还是不是???
不管是不是他都是等比数列
若是,则cn=2^n Tn=(2-2^(n+1))/(1-2)=2^(n+1)-2
若不是,则cn=(-d1)^(bn/4)+26=2^(n-26)+26 Tn=(2^(-25)-2^(n-25))/(1-2)+26*n
=2^(n-25)-2^(-25)+26n

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亲 你给的题是不是对的哦 我算出来k是个分数

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