Question

$p_n \to r, q_n \to r, \alpha_n , \beta_n \in [0,1]$ and $\alpha_n + \beta_n =1$ for all $n$, prove that $p_n \alpha_n +q_n \beta_n\to r$

score 40 · Answer 1 · 2026-04-16 19:52:14

$p_n \to r, q_n \to r, \alpha_n , \beta_n \in [0,1]$ and $\alpha_n + \beta_n =1$ for all $n$, prove that $p_n \alpha_n +q_n \beta_n\to r$

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49

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List Question

$p_n \to r, q_n \to r, \alpha_n , \beta_n \in [0,1]$ and $\alpha_n + \beta_n =1$ for all $n$, prove that $p_n \alpha_n +q_n \beta_n\to r$

$f(x)=\lim f_n(x).$

Proving a set is connected in $\mathbb{R}^2$

A property for real valued functions

smooth ( complex valued) functions "divisible" by $\mathbb{z}^{2}$

Prove the characteristic function of Cantor set is continuous almost everywhere.

Suppose that every sequence in A has a convergent sub-sequence. Prove that A is bounded.

Lipschitz function with $0$ derivative a.e. is constant on connected components

Sets homeomorphic to convex sets

Pointwise congergent subsequence?

Are geometric lines and $\mathbb{R}$ formally identical objects?

Finite Overlap Covers and Integration

Convergence in $L^2$ does not imply convergence in $L^\infty$

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Show that the series $\sum_{n=0}^\infty (-1)^n \frac{1}{(n+1)^p}$ converges and converges absolutely

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