1+3+6+10 =20
The sum of the first n cubed numbers is the square of the nth triangular number.
171700
The sum of the first four prime numbers is 17.
The sum is 17.
When you add two consecutive triangular numbers, the result is a perfect square. For example, the first two triangular numbers are 1 (T1) and 3 (T2), and their sum is 4, which is (2^2). In general, the sum of the (n)-th triangular number (T_n) and the ((n+1))-th triangular number (T_{n+1}) equals ((n+1)^2). This relationship holds for all pairs of consecutive triangular numbers.
It is 46.
The sum of the first n cubed numbers is the square of the nth triangular number.
171700
The sum of the first four prime numbers is 17.
The sum of the first four prime numbers is 17.
the answer is of course 12
The sum is 17.
When you add two consecutive triangular numbers, the result is a perfect square. For example, the first two triangular numbers are 1 (T1) and 3 (T2), and their sum is 4, which is (2^2). In general, the sum of the (n)-th triangular number (T_n) and the ((n+1))-th triangular number (T_{n+1}) equals ((n+1)^2). This relationship holds for all pairs of consecutive triangular numbers.
16
twenty
A trisquare is a specific type of mathematical object that relates to the concept of squares and triangular numbers. It is defined as a number that can be expressed as the sum of the first ( n ) triangular numbers, which themselves are formed by the formula ( T_n = \frac{n(n+1)}{2} ). This means a trisquare can be represented as ( S_m = T_1 + T_2 + ... + T_m ), where ( S_m ) is the sum of the first ( m ) triangular numbers. Trisquares have interesting properties in number theory and combinatorics.
1+1+1+1+1+=5 * * * * * The question did not ask for the sum of the first counting number five times! The sum of the first 5 counting numbers is 1+2+3+4+5 = 15. Such sums are known as triangular numbers.