1. Let X =5, X2= 2, X3-3, X4=-5, X5-7. Please find the following sums. Please WRITE OUT what you will add. Start by writing out the sum using X, X2, X3, X4, and X5, and THEN plug in the numbers. Do NOT just write down a number - even if you are completely comfortable with summation rules! 5 (a) E Xi i=1 4 w (b) [ Xi i=3 5 (c) X; 2 i=1 5 (d) [(X +0.5) i=1 5 (e) Xi + 0.5 i=1 5 (f) (3 X; + 4) i=1 1 5 (g) ( X; + 0.5)2 i=1 5 (h) (1/5) [ (X -0.5)] i=1 2. Write the following in summation notation: (a) (X + 3) + (X + 3) + (X3 + 3) +...+ (XN-1 + 3) + (XN + 3) (b) (X + 1) + (X2 + 2) + (X3 + 3) +...+ (XN-1 + N-1) + (XN + N) (c) (X + 3) + (x + 3) + (X3 + 3) +...+ (XN-1 + 3) + (XN + 3) (d) (X + Y) + (X2 + Y) + (X3 + Y3) +...+ (XN-1 + YN-1) + (XN + YN) (e) (X + X Y) + (X + XY) + (X3 + X3Y3) +...+ (XN-1 + XN-1YN-1) + (XN + XN YN) (f) (X-m) + (x - m) + (x3 - m) +...+ (XN-1 - m) + (XN - m) (g) (1/N) [(X - m) + (X - m) + (x3 - m) +...+ (XN-1 - m) + (XN - m)] (h) c(Xm) + c(X - m) + c(X3 - m) +...+ c(XN-1 - m) + c(XN-m) (i) X/(1+r) + X /(1+r) + X3 /(1+r) +...+ XT-1 /(1+r) -1 + X/(1+r)T Please simplify the following product: (j) X(1+r)(1+r)(1+r)(1+r)