Question

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pls ns this que pls

Find the sum of the series 3.5/5.10+3.5.7/5.10.15+3.5.7.9/5.10.15.20+......................infinity.

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Answer 1

Qᴜᴇsᴛɪᴏɴ :-

Find the sum of the series :- 3.5/5.10+3.5.7/5.10.15+3.5.7.9/5.10.15.20+......................infinity.

Sᴏʟᴜᴛɪᴏɴ :-

Let the series Equal to S .

→ S = 3.5/5.10 + 3.5.7/5.10.15 + 3.5.7.9/5.10.15.20 +....

Adding 1 + (3/5) Both sides we get,

→ 1+ (3/5) + S = 1 + 3/5 3.5/5.10 + 3.5.7/5.10.15 + 3.5.7.9/5.10.15.20 +....

Splitting The RHS part now,

→ 1 + (3/5) + S = 1 + (3/1)(1/5) + (3.5/1.2)(1/5)^2 + (3.5.7/1.2.3)(1/5)^3 + ...

→ 8/5 + S = [1 - (2/5)]^(-3/2)

→ 8/5 + S = [(3/5)]^(-3/2)

→ 8/5 + S = (5/3)^(3/2)

→ S = (5/3)^(3/2) - (8/5) (Ans.)

Answer 2

Qᴜᴇsᴛɪᴏɴ :-

Find the sum of the series :- 3.5/5.10+3.5.7/5.10.15+3.5.7.9/5.10.15.20+......................infinity.

Sᴏʟᴜᴛɪᴏɴ :-

Let the series Equal to S .

→ S = 3.5/5.10 + 3.5.7/5.10.15 + 3.5.7.9/5.10.15.20 +....

Adding 1 + (3/5) Both sides we get,

→ 1+ (3/5) + S = 1 + 3/5 3.5/5.10 + 3.5.7/5.10.15 + 3.5.7.9/5.10.15.20 +....

Splitting The RHS part now,

→ 1 + (3/5) + S = 1 + (3/1)(1/5) + (3.5/1.2)(1/5)^2 + (3.5.7/1.2.3)(1/5)^3 + ...

→ 8/5 + S = [1 - (2/5)]^(-3/2)

→ 8/5 + S = [(3/5)]^(-3/2)

→ 8/5 + S = (5/3)^(3/2)

→ S = (5/3)^(3/2) - (8/5) (Ans.)