Question

What can be the sum S= k=1 to k=100∑(-1)^[k(k+1)÷2] k^2 ?

Answer 1

Answers :-

Hey mate...

here is your answer:-

Step-by-step explanation:

make life simpler avoiding the situation of dealing with the -1 power term. Split the sum into 4 parts. take index k from 0 to n and evaluate summations of squares of 4k, 4k+1, 4k+2 and 4k+3. for the 4k + i terms probably the index should be till n-1 because you don’t want the squares after 4n. summation of square terms is easily given by the formula

S = n( n+1)(2n+1)/6.

The powers of -1 will be 1 -1 -1 and 1 so add signs accordingly. Try it out. it should probably be something like this

Hope this helps..