Question

find
the sum
of
40 terms, 1+3+9+2 7+.
3 in gp​

Answer 1

Answer:

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Answer 2

Answer:

The given series X=1+2+3+4+5+8+7+16+9+....

This is sum of 2 series X

1

and X

2

X

1

+X

2

=X

X

1

=1+3+5+7+9+.......

X

2

=2+4+8+16+.......

X

1

is an AP with first term 1 and common difference 2

X

2

is a GP with first term 2 and common ratio 2

Now for sum up to 40 term for X, we need to find sum of first 20 terms of the GP and first 20 terms of AP.

Sum of AP =S

AP

=

2

20

(2+(20−1)2)=10(2+38)=400

Sum of GP =S

GP

=

1−2

2(1−2

20

)

=−2+2

21

So, Sum X =400−2+2

21

= 398+2

21