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

###### Question details

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}* =

*an*

^{2}+

*bn*+

*c*with some unknown

*a,b,c*and then fix these coefficients by considering

*S*for different values of

_{n}*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.