Use the Principle of mathematical induction to prove that:(1)|z_1z_2z_3⋯ ⋯ z_n|=|z_1|
【题目】Use the principle of mathematical induction toprove that the following propositions (conjectures) are true for all positive integers n:Note: You should remember the result from(1):1+2+3+……+nn(n+) foallnin +(1 ∑_(i=1)^ni=(n(n+1))/2i=1(2∑_(i=1)^ni(i+1)=(n(...
【题目】Use the principle of mathematical induction to prove that statement is true for all natural n umbers n.6" -1 is divisible by 5 相关知识点: 试题来源: 解析 【解析】 6" -1 is divisible by 5 1. Show sn is true for n=1. S_n:6^n-1=5m S_1:6^1-1=5m 6-1=5m 5 5m ...
Proof: (By the principle of mathematical induction)(1) If n=1, u_1= 2(3^(1-1))-1=2-1= 1 which is true so P_1 is true.(2) If P_k is true, then u_k =2(3^(k-1))- 1 andu_(k+1)=2 + 3u_k=2 +3[2(3^(k-1))-1] Using P_k=2 + 6(3^(k-1))-3= 6...
Use the principle of mathematical induction to prove that the following propositions (conjectures) are true for all positive integers n:Note: You should remember the result from (1):1+2+3+⋯⋯+n=(n(n+1))2 for all n in ^+.
Use the principle of mathematical induction to prove that statement is true for all natural numbers n.6^n-1 is divisible by 5 相关知识点: 试题来源: 解析 6^n-1 is divisible by 51. Show S_n is true for n=1. S_n: 6^n-1=5mS_1: 6^1-1=5m6-1=5m5=5m1=m Verified2. Assume...
(k+ 1)-3(k+ 1)}= 7(k+1)-7.3k+ 7.3k-3(k+1)= 4(7m + 3k), which is clearly divisible by 4...P(k+ 1): {7(k+1)-3(k + 1)} is divisible by 4.→P(k + 1) is true, whenever P(k) is true.Hence, by the principle of mathematical induction, P(n) is true for ...
【题目】Prove the following propositions using the principle of mathematical induction∑_(i=1)^n((2i-1)^2)=(n(2n+1)(2n-1))/3n , n≥1=1∈Z 相关知识点: 试题来源: 解析 【解析】proof: (By the principle of mathemamtical induction)1. If n=1, as=1, and=(1(2⋅1+1)(2⋅1...
proof: (By the principle of mathemamtical induction)1. If n=1, LHS =1, and RHS =(1*4)(4*2*3)=16, ∴ P_1 is true.2. If P_k is true, then1(1*2*3)+1(2*3*4)+⋯+1(k*(k+1)*(k+2))=(k(k+3))(4(k+1)(k+2))Thus 1(1*2*3)+1(2*3*4)+⋯+1(k*(...
【解析】proof: (By the principle of mathematical induction)1. If a=1, Las=1, and RHs=2!-1=1, ∴.P is true.2. If p is true, then1*1!+2*2!+3*3!+⋯+k*k! =(k+1)!-1 Thus1*1!+2*2!+3*3!+⋯+k! +(k+1)*(k+1) =(k+1)!-1+(k+1)*(k+1)! =[(k+1)...