【题目】Use mathematical induction to prove that eachstatement is true for each positive integer n.∑_(i=1)^n2^i^j=2^(n+1)=2 相关知识点: 试题来源: 解析 【解析】∑_(i=1)^n(2^i) Compute the general progression formula of 2r=2, a_1=2^ir=2, a_i=2^iGeometric sequence sum ...
In Exercises, use mathematical induction to prove that each statement is true for every positive integer n.(ab)^n=a^nb^n 相关知识点: 试题来源: 解析 S_1: (ab)^1=a^1b^1; S_k: (ab)^k=\ a^kb^k; S_(k+1): (ab)^(k+1)=a^(k+1)b^(k+1); S_(k+1) can be obtain...
Use mathematical induction to show that when n is an exact power of 2, the solution of the recurrence T(n)= \left\{\begin{matrix} 2& if\ n= 2\2T(n/2) + n &if\ n=2^k,\ for\ k > 1 \end{matrix}\right.\is\ t(n)= n\lg n ...
Use the principle of mathematical induction to show that 5^(2+1)+3^(n+2).2^(n-1) divisible by 19 for all natural number n.
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 ^+.
In Exercises, use mathematical induction to prove the property for all positive integers n.If , , , , then. 相关知识点: 试题来源: 解析 In order to prove the given property for all positive integers n, we must first prove that it holds for n=1:Then, we must prove that if the ...
In order to prove the given property for all positive integers n, we must first prove that it holds for n=1:(x_1)^1=x_1^(-1)1/(x_1)=1/(x_1)Then, we must prove that if the property holds for some positive integer k, then it holds for k+1 as well:(x_1x_2x_3⋯x_...
Use mathematical induction to prove the statement is true for all positive integers n . The integer n^3 + 2n is divisible by 3 for every positive integer n . By induction, prove that 3^n - 1 is divisible by 2 and is valid for all positive integers. ...
Follow the outline below and use mathematical induction to prove the Binomial Theorem:(a+b)^n=(pmatrix) n 0(pmatrix) a^n+(pmatrix) n 1(pmatrix) a^(n-1)b+(pmatrix) n 2(pmatrix) a^(n-2)b^2+⋯ +(pmatrix) n n-1(pmatrix) ab^(n-1)+(pmatrix) n n(pmatrix) b^n....
Abstract: On the way to prove inequality. Commonly used analysis, synthesis method, comparative law, with the method, discriminant method, by contradiction, mathematical induction, using the known inequality method, using the known changes in the function of, for element method, scaling method, adju...