Question

1x30+2x29+3x28+4x27+.....................+27x4+28x3+29x2+30x1=?
porfa ayuda en eso

Answer 1

                       $?=2(1\times 30+2\times 29+\cdots+15\times 16)\\ \\ ?=2\sum\limits_{n=1}^{15}n(31-n)\\ \\ \\ ?=2\sum\limits_{n=1}^{15}31n-n^2\\ \\ \\ ?=2\sum\limits_{n=1}^{15}31n-2\sum\limits_{n=1}^{15}n^2\\ \\ \\ ?=62\sum\limits_{n=1}^{15}n-2\sum\limits_{n=1}^{15}n^2\\ \\ \\ ?=62\left(\dfrac{15\times16}{2}\right)-2\left(\dfrac{15\times16\times31}{6}\right)\\ \\ \\ ?=15\times16\left(31-\dfrac{31}{3}\right)\\ \\ \\ ?=15\times16\times \dfrac{62}{3}\\ \\ ?=80\times 62\\ \\ \boxed{?=4960}$