What would be the simplest way to prove that ∞∑i=1i2i converges?
Answer
Another possible way : consider ∞∑i=1ixi=x∞∑i=1ixi−1=xddx(∞∑i=1xi)=xddx(x1−x)=x(1−x)2
Now, replace x by 12 to get 2.
The same procedure would apply to ∞∑i=1iai=a(a−1)2
What would be the simplest way to prove that ∞∑i=1i2i converges?
Answer
Another possible way : consider ∞∑i=1ixi=x∞∑i=1ixi−1=xddx(∞∑i=1xi)=xddx(x1−x)=x(1−x)2
The same procedure would apply to ∞∑i=1iai=a(a−1)2
I have injection f:A→B and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...
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