Show that ∑+∞n=1n2n=2. I have no idea to solve this problem. Anyone could help me?
Answer
Consider the following
11−x=∑k≥0xk
The series converges for |x|<1
Differentiating both sides we have
1(1−x)2=∑k≥1kxk−1
x(1−x)2=∑k≥1kxk
Now put x=12
2=∑k≥1k2k
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