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Sequences and Series question

2023 · 29 Jan · Shift 2 · Q43

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JEE Main
Mathematics
Sequences and Series
2023 · 29 Jan · Shift 2 · Q43

Sequences and Series question

2023 · 29 Jan · Shift 2 · Q43

JEE MainMathematicsSequences and SeriesNumerical+4 / −1

Let

\{ {a_k}\}

and

\{ {b_k}\} ,k \in N

, be two G.P.s with common ratios

{r_1}

and

{r_2}

respectively such that

{a_1} = {b_1} = 4

and

{r_1} \lt {r_2}

. Let

{c_k} = {a_k} + {b_k},k \in N

. If

{c_2} = 5

and

{c_3} = {{13} \over 4}

then

\sum\limits_{k = 1}^\infty {{c_k} - (12{a_6} + 8{b_4})}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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