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Question

It is given that 114+124+134+....=π490. Then 114+134+154+...is equal to


A

π496

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B

π445

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C

89π90

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D

None of these

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Solution

The correct option is A

π496


Explanation for correct option:

Finding the value of given terms:

Let us consider 114+134+154....=S .

Therefore we have,

114+124+134+.....=π490Letussplittheoddandeventerms114+134+154+...+124+144+164+....=π490S+124114+124+134+....=π490S+124×π490=π490givenS=π490-π490×16=π4901-116=π490×1516S=π496

Therefore, S=π496.

Hence, option (A) is the correct answer.


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