Sum to infinity of the series 1-4-5-7-52-10-53- is

The correct option is C Let S=1+4/5+7/5^2+10/5^3+..... ⇒1/5S = 1/5+4/5^2+7/5^3+.... On subtraction, 4/5S =1 +3/5+3/5^2+3/5^3+... ⇒ S =7/4×5/4=35/16 ...

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Byju's Answer

Standard XI

Mathematics

Sigma n

Sum to infini...

Question

Sum to infinity of the series $1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + . . . . . i s$

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Solution

The correct option is C
$L e t S = 1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + . . . . . \Rightarrow \frac{1}{5} S = \frac{1}{5} + \frac{4}{5^{2}} + \frac{7}{5^{3}} + . . . . O n s u b t r a c t i o n, \frac{4}{5} S = 1 + \frac{3}{5} + \frac{3}{5^{2}} + \frac{3}{5^{3}} + . . . \Rightarrow S = \frac{7}{4} \times \frac{5}{4} = \frac{35}{16}$

Suggest Corrections

Sum to infinity of the series 1+45+752+1053+.....is

The correct option is C Let S=1+45+752+1053+.....⇒15S=15+452+753+....On subtraction,45S=1+35+352+353+...⇒S=74×54=3516

Sum to infinity of the series $1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + . . . . . i s$