Sn=2/2+3/2²+4/2³+····+(n+1)/(2^n) 求Sn.
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![Sn=2/2+3/2²+4/2³+····+(n+1)/(2^n) 求Sn.](/uploads/image/z/3815312-32-2.jpg?t=Sn%3D2%2F2%2B3%2F2%26%23178%3B%2B4%2F2%26%23179%3B%2B%C2%B7%C2%B7%C2%B7%C2%B7%2B%28n%2B1%29%2F%282%5En%29+%E6%B1%82Sn.)
Sn=2/2+3/2²+4/2³+····+(n+1)/(2^n) 求Sn.
Sn=2/2+3/2²+4/2³+····+(n+1)/(2^n) 求Sn.
Sn=2/2+3/2²+4/2³+····+(n+1)/(2^n) 求Sn.
Sn=2/2+3/2²+4/2³+····…+n/2^(n-1)+(n+1)/(2^n)
2Sn=2+3/2+4/2²+5/2³+……+(n+1)/2^(n-1)
下减上得
Sn=2+[(1/2)+(1/4)+(1/8)+……+[1/2^(n-1)]]-(n+1)/2^n
=2+{1/2[1-(1/2)^(n-1)]/(1-1/2)}-(n+1)/2^n
=2+1-1/[2^(n-1)]-(n+1)/2^n
=3-2/2^n-(n+1)/2^n
=3-(2+n+1)/2^n
=3-[(3+n)/2^n]