This website is for students who are interested in mathematics !!
I'll start of the website with an algebraic equation.....
What is n + n^2 + n^3 + n^4 +. . . + n^x = ?
= n(1+ n + n^2 + n^3 +. . .n^x-1)
= n(1 + n (n + n^2 +. . .n^x-1))
= n(1+n(1+n+. . .n^x-1))
I'll start of the website with an algebraic equation.....
What is n + n^2 + n^3 + n^4 +. . . + n^x = ?
= n(1+ n + n^2 + n^3 +. . .n^x-1)
= n(1 + n (n + n^2 +. . .n^x-1))
= n(1+n(1+n+. . .n^x-1))
= n(1+n(1+n(1+n . . . x-1 times))) ----------------------(1)
For example
(i) Let
n=2, x=4
For example
(i) Let
n=2, x=4
n + n^2 + n^3 + n^4 = 2+4+8+16 = 30 ---------------------(2)
From (1),
n + n^2 + n^3 + n^4 = 2(1+2(1+2(1+2)))
= 2(1+2(1+6))
= 2(1+14)
= 2(15)
= 30 = (2)
(ii)Let
n=17,x=3
n + n^2 + n^3=17(1+17(1+17))
=17(1+306)
=17(307)
=5219
But it is difficult to calculate using the ordinary method because, 17+17^2+17^3
=17+289+4913
=5219