JEE Main 2022 (Online) 25th June Morning Shift | Sequences and Series Question 99 | Mathematics | JEE Main - ExamSIDE.com

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JEE Main 2022 (Online) 25th June Morning Shift

Numerical

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Out of Syllabus

For a natural number n, let $${\alpha _n} = {19^n} - {12^n}$$. Then, the value of $${{31{\alpha _9} - {\alpha _{10}}} \over {57{\alpha _8}}}$$ is ___________.

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2

JEE Main 2022 (Online) 25th June Morning Shift

Numerical

+4

-1

Out of Syllabus

The greatest integer less than or equal to the sum of first 100 terms of the sequence $${1 \over 3},{5 \over 9},{{19} \over {27}},{{65} \over {81}},$$ ...... is equal to ___________.

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3

JEE Main 2021 (Online) 31st August Evening Shift

Numerical

+4

-1

The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is ____________.

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4

JEE Main 2021 (Online) 31st August Evening Shift

Numerical

+4

-1

Out of Syllabus

If $$S = {7 \over 5} + {9 \over {{5^2}}} + {{13} \over {{5^3}}} + {{19} \over {{5^4}}} + ....$$, then 160 S is equal to ________.

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