1 2 2 2 3 2 n n formula

1 2 2 2 3 2 n n formula The series sum limits k 1 n k a 1 a 2 a 3 a cdots n a gives the sum of the a text th powers of the first n positive numbers where a and n are positive integers Each of these series can be calculated

Prove that 1 2 2 2 3 2 1 n 1 n 2 1 n 1 frac n n 1 2 whenever n is a positive integer using mathematical induction Please look at this expression 1 2 2 2 3 2 4 2 cdots 1 n 1 n 2 I found this expression in a math book It asks us to find a general formula for calculate it with n

1 2 2 2 3 2 n n formula

1 2 2 2 3 2 n n formula
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Find The Sum Of The Following 1 Toppr
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This is an arithmetic series and the equation for the total number of times is n 1 n 2 Example if the size of the list is N 5 then you do 4 3 2 1 10 swaps and Using the difference of two squares we can write 12 22 32 42 2n 1 2 2n 2 12 22 32 42 2n 1 2 2n Now 3 7 11 4n 1 is an

Explanation using the method of proof by induction this involves the following steps prove true for some value say n 1 assume the result is true for n k prove true Did Gauss derive the 1 2 3 ldots n 2 n 1 n frac n n 1 2 formula in elementary school If so what biography of Gauss discusses it

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The partial sums of the series 1 2 3 4 5 6 are 1 3 6 10 15 etc The nth partial sum is given by a simple formula This equation was known Example 1 For all n 1 prove that 12 22 32 42 n2 n n 1 2n 1 6 Let P n 12 22 32 42 n2 1 2 1 6 Proving for n 1 For n 1 L H S 12 1 R H S 1 1 1 2 1 1 6 1

Question2 Prove the following by using the principle of mathematical induction 13 23 33 n3 1 2 2 Let P n 13 23 33 43 n3 1 2 2 For n 1 L H S 13 1 R H S 1 1 1 2 2 The formula for the sum of squares of first n natural numbers is given by 1 2 2 2 3 2 n 2 n n 1 2n 1 6 eqn 1 and as far as the proof is

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1 2 2 2 3 2 n n formula - Explanation using the method of proof by induction this involves the following steps prove true for some value say n 1 assume the result is true for n k prove true