Let $$a_1, a_2, ...$$ be integers such that $$a_1 - a_2 + a_3 - a_4 + .... + (-1)^{n - 1} a_n = n,$$ for all $

Question

Let $$a_1, a_2, ...$$ be integers such that $$a_1 - a_2 + a_3 - a_4 + .... + (-1)^{n - 1} a_n = n,$$ for all $$n \geq 1.$$ Then $$a_{51} + a_{52} + .... + a_{1023}$$ equals

Accepted Answer

1. a 1 − a 2 + a 3 − a 4 + . . . . + ( − 1 ) n − 1 a n = n a_1 - a_2 + a_3 - a_4 + .... + (-1)^{n - 1} a_n = n a 1 ​ − a 2 ​ + a 3 ​ − a 4 ​ + .... + ( − 1 ) n − 1 a n ​ = n It is clear from the above equation that when n is odd, the co-efficient of a is positive otherwise negative. a 1 − a 2 = 2 a_1 -

Let $a_1, a_2, ...$ be integers such that
$a_1 - a_2 + a_3 - a_4 + .... + (-1)^{n - 1} a_n = n,$ for all $n \geq 1.$
Then $a_{51} + a_{52} + .... + a_{1023}$ equals

Let $a_1, a_2, ...$ be integers such that
$a_1 - a_2 + a_3 - a_4 + .... + (-1)^{n - 1} a_n = n,$ for all $n \geq 1.$
Then $a_{51} + a_{52} + .... + a_{1023}$ equals