Suppose the two series of real numbers ∑ݑΰݑ۠and ∑ݑϰݑ۠are both

Question

2. a) Suppose the two series of real numbers ∑ݑΰݑ۠and ∑ݑϰݑ۠are both divergent. Prove or disprove the following, i) ∑ݑ߰ݑΰݑ۠is divergent for any given non zero real number ݑ߬ ii) ∑(ݑΰݑۢȒݑϰݑ۩ is divergent, iii) ∑(ݑΰݑ۫ݑϰݑ۩ is divergent