Question
The sum of infinite terms of the following series
1 + 45 + 752 + 1053 + ...........∞ will be
1 + 45 + 752 + 1053 + ...........∞ will be
Answer: Option D
:
D
Let the sum to infinity of thearithmetic-geometric series be
S = 1 + 4 . 15 + 7. 152 + 10. 153 +........
⇒15S =15+ 4.152+ 7.153+...........
Subtracting (1 - 15)S = 1 + 3.15 + 3.152 + 3.153 + .......
= 1 + 3(15 +152 + ..............)
⇒45S = 1 + 3.15(11−15) = 1 +34 =74⇒ S =3516.
Aliter :Use direct formula S∞ =ab1−r +dbr(1−r)2
Here a = 1, b = 1, d = 3, r =15, therefore
S∞ =11−15 +3×1×15(1−152) =54 +351625 =54 +1516 =3516.
Aliter:Use S = [1 + r1−r × diff. of A.P.]11−r
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:
D
Let the sum to infinity of thearithmetic-geometric series be
S = 1 + 4 . 15 + 7. 152 + 10. 153 +........
⇒15S =15+ 4.152+ 7.153+...........
Subtracting (1 - 15)S = 1 + 3.15 + 3.152 + 3.153 + .......
= 1 + 3(15 +152 + ..............)
⇒45S = 1 + 3.15(11−15) = 1 +34 =74⇒ S =3516.
Aliter :Use direct formula S∞ =ab1−r +dbr(1−r)2
Here a = 1, b = 1, d = 3, r =15, therefore
S∞ =11−15 +3×1×15(1−152) =54 +351625 =54 +1516 =3516.
Aliter:Use S = [1 + r1−r × diff. of A.P.]11−r
Was this answer helpful ?
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