Question: i need help with these please problem 4 calculate 1...

I need help with these please.

Problem 4.

Calculate

1 + 2 + 3 + ··· + 98 + 99 + 100

by deriving a general formula for . To that end start with the conjectural form for S_n = an² + bn + c with some unknown a,b,c and then fix these coefficients by considering S_n for different values of n.

Problem 5.

Check the expression for

by showing that (1 + x) × (1 + x)^a = (1 + x)^a+1. If the case of general a poses challenge, check this expression for a = 3.