1 + 2/1 - 6/5 + 12/7 - 20/9 + 30/11 - 42/13 can be simplified by finding a common denominator and then adding the fractions together.
To find a common denominator, we need to find the least common multiple (LCM) of 1, 5, 7, 9, 11, and 13 which is 15,015.
Rewriting the fractions with the common denominator:
(1 * 15,015/1 * 15,015) + (2 * 15,015/1 * 15,015) - (6 * 15,015/5 * 15,015) + (12 * 15,015/7 * 15,015) - (20 * 15,015/9 * 15,015) + (30 * 15,015/11 * 15,015) - (42 * 15,015/13 * 15,015)
Simplifying:
15,015/15,015 + 30,030/15,015 - 180,090/15,075 + 180,180/15,075 - 300,300/15,135 + 450,450/16,515 - 630,630/15,195
Adding the fractions:
= (15,015 + 30,030 - 180,090 + 180,180 - 300,300 + 450,450 - 630,630)/15,195
= 15,555/15,195
The final answer is approximately 1.024.
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