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determine if the following infinite series converage or diverage, and explain why
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- In the expansion of (5x+3y)n , each term has the form (nk)ankbk ,where k successively takes on the value 0,1,2....,n. If (nk)=(72) what is the corresponding term?if we had some f(z)= an infinite sum of z^n how would we solve this?If s(n)=3n2−3n+5s(n)=3n2−3n+5, then s(n)=2s(n−1)−s(n−2)+cs(n)=2s(n−1)−s(n−2)+c for all integers n≥2n≥2. What is the value of c ?
- What are the lower bound and upper bound of the given problem 1c? Is it 0 or 1? P(x is 40 or fewer senior) = binomcdf (n=50, p=0.72, LB=?, UB=?) = 0.9260We now need to attempt to find an exact value for n such that P(r ≥ 1) = 0.99. Clearly, if the bank has any chance of detecting a burglar they will need to have at least one alarm installed. So, we know that, minimally, n must be at least 1.Since n must be at least 1, suppose we start by trying n = 2, where there will be two alarms. When there are two alarms, r ≥ 1 means either one or both alarms could detect the burglar. If neither alarm detects the burglar it is considered a failure. Therefore, P(r ≥ 1) can be calculated using either of the following formulas. P(r ≥ 1) = P(1) + P(2) P(r ≥ 1) = 1 − P ( ___ ) fill in the blank(a) Find the sum to infinity of the series 1-3x+5x\power{2}-7x\power{3}+....∞ where 0<|x|<1 (b) Find the sum of the series 1×n+2(n-1)+3(n-2)+......+ (n-1)×2+n×1
- If H1: μ1 – μ0 < 0, then zobs = -1 has a lower p-value than zobs =1. True or false?(b) Prove or disprove the statement∀n ∈ N: ln(n + 1) ≤ 1 +1/2+ · · · +1/n≤ 1 + ln(n)Provide NEAT and COMPLETE solutions for the following problems. 4. Let n ∈ Z. Prove that if n is odd, then n = 4k + 1 or n = 4k + 3 for someinteger k.