Question

find the sum of the following series 1+√3+3+.........upto 8 terms

Answer 1

Give G.P series,
1+√3+3.................
common ratio=a2/a1=√3/1
common ratio=√3
sum of n terms=Sn={a(1-r^n)}/(1-r)
Here,
a=1 , r=√3 and n=10
Now we have,
S10={1(1-√3^10)}/(1-√3)

S10={1-243}/(1-√3)

S10={-242(1+√3)}/(1-√3)(1+√3)

S10={-242(1+√3)}/(-2)

S10=121(1+√3)

Hence sum of 10 terms of given G.P series=121(1+√3).



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Answer 2

Answer:

G.P. =1+√3+3+...

a=1 r=√3/1=√3 n=8

Now,Sn=a(rn-1)/r-1

1(√3^8-1)/√3-1

√3×√3×√3×√3×√3×√3×√3×√3-1/√3-1

81-1/√3-1

80/√3-1

80/√3-1×√3+1/√3+1

80√3+1/√3²-1²

80(√3+1)/3-1

80√3+1/2

40√3+1

Hence,S8=40(√3+1) or 40(√3+1)