## Realated Questions

A child was asked to add first few natural numbers (that is, 1 + 2 + 3......) so long his patience permitted. As he stopped, he gave the sum as 575. When the teacher declared the result wrong the child discovered he had missed one number in the sequence during addition. The number he missed was:

- Let S denote the infinite sum 2 + 5x + 9x
^{2}+ 14x^{3}+ 20x^{4}+ ..., where | x | < 1 and the coefficient of x^{n-1}is [n(n + 3)]/2, (n = 1, 2, ...). Then S equals: In a survey of political preference, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one?