Show that the sum of the squares of the first n natural numbers is given by,S=(n(n+1)(2n+1))/6

Q: 2(7-3x) =1/4

A: The equation is, 27-3x=14 Solve for x as, 27-3x=12227-3x=2-27-3x=-23x=7+23x=9x=93x=3

Q: You are given a real number N. How should you write it as a sum of two real numbers so that their…

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Q: For how many different positive integer values of m does (mx - 10)^2 = 0 have integer solutions ?

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Q: (n^2-n)+((n-1)^2-(n-1))+....+(1^2-1) =n(n+1)(2n+1)/6 - n(n+1)/2

A: We shall first derive the formulas for sum of first n natural numbers and sum of squares of first n…

Q: An instructor of mathematics wishes to determine the relationship of grades on a final examination…

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Q: find  3/4 + 1/8

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Q: Find the x3 term in (x-1) (2x-2)4   4=n, 5 terms

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Q: Find a counterexample to the statement that every positive integer can be written as the sum of the…

A: Claim: Every positive integer can be written as the sum of the squares of three integers. The given…

Q: = 5 Find a3, a4, and as for the recursive formula an = an-1 +3an-2 if a1 = 2 and a2

A: given   recursive formula is an= an-1+3an-2and   a1=2   ,  a2=5then we have to find  a3 , a4  , a5…

Q: Use the approach in Gauss problem to find the sum of 8+17+26+35+...+890

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Q: find the 6th term of (4h-j)8

A: formula used is   tr+1=Crn(a)n-r(b)r  for  (4h-j)8, a=4h ,b=-j and n=8

Q: 9 Solve for x. (17x-23) 81* 74*

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