Write the following using a summation sign with an appropriate index?

a) Y3+ Y4.... + Y15
Ans: 15Σi=3Yi

b) Y21+ Y22+ Y23Y24
Ans: 4Σi=1Y2i

c) (Y1-u)2+ (Y2-u)2+ (Y3-u)2
Ans: 3Σi=1(Yi-u)2

d) bY20+ bY21.... + bY30
Ans: 30Σi=20Yi

ii) Expand the following summation and product signs?

a)5Σi=1Yi 
Ans: = Y1+ Y2+ Y3+ Y4+Y5

b)8Σi=5(Yi-u)
Ans: = (Y5-u)+(Y6-u)+(Y7-u)+(Y8-u)

c)3Σi=1Y2i
Ans: = Y21+ Y22+ Y23

d)4Σi=2(Yi-9)
Ans: = (Y2-9)+(Y3-9)+(Y4-9)

e)3πi=1Yi
Ans: = Y1+ Y2+ Y3

f)6πi=3(aYi)2
Ans: = a2Y23+ a2Y24+ a2Y25+ a2Y26

g)4πi=2(Xi-Yi)
Ans: = (X2-Y2)+ (X3-Y3)+ (X4-Y2)

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