Write a program to compute 1/22/33/4n/n1 with a given n input by console (n>0) Example If the following n is given as input to the program 5 Then, the output of the program should be 355 in Python by Dhineshbabu • 130 points •The sum of the first n squares, 1 2 2 2 n2 = n ( n 1) (2 n 1)/6 For example, 1 2 2 2 10 2 =10×11×21/6=385 This result is usually proved by a method known as mathematical induction, and whereas it is a useful method for showing that a formula is true, it does not offer any insight into where the formula comes from Instead weView solution If a n 1 = a n − n 2 n and a 1 = 3 then the value of ∣ a 2 0 − a 1 5 ∣ =
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1*2*3*4*5*n formula
1*2*3*4*5*n formula-To do this, we will fit two copies of a triangle of dots together, one red and an upsidedown copy in green Eg T (4)=1234 Let term of the series 1 (1 2) (1 2 3) (1 2 3 4) (1 2 3 n) be denoted as an an = Σ n1 = = Sum of nterms of series Σ n1 a n = Σ n1 = Σ Σ = * * = Below is implementation of above approach
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The hypothesis of Step 1) " The statement is true for n = k " is called the induction assumption, or the induction hypothesis It is what we assume when we prove a theorem by induction Example 1 Prove that the sum of the first n natural numbers is given by this formula 1 2 3 n = 3 Add a comment 6 According to Wikipedia S = n * (n 1) * (2*n 1) / 6 It is easy to prove this using induction Share edited Aug 1 '12 at 1745 For those of you who are unfamiliar with this series, which has come to be known as the Ramanujan Summation after a famous Indian mathematician named Srinivasa Ramanujan, it states that if you add all the natural numbers, that is 1, 2, 3, 4, and so on, all the way to infinity, you will find that it is equal to 1/12 Yup,
Find the sum ∑ r = 1 n r (r 1) 1 2 2 2 3 2 r 2 ?Making Equivalent Fractions 43 Rewrite the two fractions into equivalent fractions Two fractions are called equivalent if they have the same numeric value For example 1/2 and 2/4 are equivalent, y/ (y1)2 and (y2y)/ (y1)3 are equivalent as well To calculate equivalent fraction , multiply the Numerator of each fraction, by its We shall prove the result by principle of mathematical induction checking for n = 1, LHS 12 = 2 RHS 1/3 * 1 * 2 * 3 = 2 Hence true for n = 1
For the proof, we will count the number of dots in T (n) but, instead of summing the numbers 1, 2, 3, etc up to n we will find the total using only one multiplication and one division! Find the sum up to n terms of the series 123 234 n(n1)(n2) In this 123 represent the first term and 234 represent the second term Examples Input 2 Output 30 123 234 = 6 24 = 30 Input 3 Output 90Solution Using the exponential formula (a m)(a n) = a mn where a = 4 4 3 $\times$ 4 2 = 4 32 = 4 5 = 1024
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The partial sums of the series 1 2 3 4 5 6 ⋯ are 1, 3, 6, 10, 15, etcThe nth partial sum is given by a simple formula = = () This equation was knownS n = 1 2 3 4 ⋯ n = k = 1 ∑ n k The elementary trick for solving this equation (which Gauss is supposed to have used as a child) is a rearrangement of the sum as follows S n = 1 2 3 ⋯ n S n = n n − 1 n − 2 ⋯ 1 \begin{aligned} S_n & = & 1 & & 2 & & 3 & \cdots & n \\ S_n & = & n & & n1 & & n2 & \cdots & 1 \\ \end{aligned} S n S n = = 1 n 2 n − 1 3 n − 2 ⋯ ⋯ n 1 Example 1 Find out the value of 5 2 – 3 2 Solution Using the formula a 2 – b 2 = (a – b)(a b) where a = 5 and b = 3 (a – b)(a b) = (5 – 3)(5 3) = 2 $\times$ 8 = 16 Example 2 4 3 $\times$ 4 2 = ?
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(1) we will prove that the statement must be true for n = k 1 Davneet Singh is a graduate from Indian Institute of Technology, Kanpur He has been teaching from the past 10 years He provides courses for Maths and Science at TeachooExample Find the nth term of AP 1, 2, 3, 4, 5, a n, if the number of terms are 15 Solution Given, AP 1, 2, 3, 4, 5, a n n=15 By the formula we know, a n = a(n1)d Firstterm, a =1 Common difference, d=21 =1 Therefore, a n = 1(151)1 = 114 = 15
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Homework Helper 3,798 94 Little ant said 1^2 2^2 3^2 2^n = 2^ (n1) This makes absolutely no sense I mean, look at it for a second firstly you failed to notice the pattern correctly since 2^n means 2^12^22^3 instead of what is shown And secondly, how can that all equal 2^ (n1) when on the left side of the equation, you(1 1/n) n (It gets more accurate the higher the value of n) That formula is a binomial, right?You know, it's not easy to answer the question without the proper context Second formula can also be used to find out number of combinations how to choose two elements out of n, or how many elements A i,j are in square matrix where i < j and probably one
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I am looking for a formula to which I can supply a number N and have it calculate 1234N I realise that I can enter 1 to N in as many cells then use SUM but this won't do for what I need to achieveDetermine if the Relation is a Function (1,2) , (2,3) , (3,4) , (4,5) , (5,6) Since there is one value of for every value of in , this relation is a function The relation is a functionAnswer to Let a_1=1 and then define a_{n1}=\\frac{7a_n}{n1} List the terms a_n and n=1,2,3,4,5 Write a formula for a_n =?
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