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Scilla [17]
2 years ago
8

Please help to find an explicit formula for calculating the sum Mn

Mathematics
1 answer:
defon2 years ago
8 0

The explicit formula for calculating the sum is

S_N=\frac{n(n-1)}{2} \cdot\frac{n(n+1)}{2}

The sum of the nth term of a sequence is expressed as;

S_n=\frac{n}{2}(2a+(n-1)d)

a is the first term

d is the common difference

n is the number of terms

For the sequence  0 + 1 + 2 + 3  +...

S_n=\frac{n}{2}(2(0)+(n-1)1)\\S_n= \frac{n}{2}(n-1)\\S_n= \frac{n(n-1)}{2}

Similarly for the sequence:

1 + 2+ 3 + 4+...

S_n=\frac{n}{2}(2(1)+(n-1)1)\\S_n= \frac{n}{2}(2+n-1)\\S_n= \frac{n(n+1)}{2}

Taking the product of the sum to get the explicit formula for calculating the sum

S_N=\frac{n(n-1)}{2} \cdot\frac{n(n+1)}{2}

Learn more here: brainly.com/question/24547297

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