Suppose a2-a3-a4-a5-a6-a7 are integers such that 57-a22-a33-a44-a55-a66-a77-where 0 - a - j for j-2-4-5-6-7- The sum a2-a3-a4-a5-a6-a7 is

The correct option is C 9 5 7 = a _ 2 2! #10;+ a _ 3 3! + a _ 4 4! + a _ 5 #10; 5! + a _ 6 6! + a _ 7 7! #10;⇒ 5 7 = 1 2 ( a _ ...

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Byju's Answer

Standard XII

Mathematics

Summation by Sigma Method

Suppose a2,...

Question

Suppose $a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}$ are integers such that
$\frac{5}{7} = \frac{a_{2}}{2!} + \frac{a_{3}}{3!} + \frac{a_{4}}{4} + \frac{a_{5}}{5!} + \frac{a_{6}}{6!} + \frac{a_{7}}{7!}$
where $0 \leq a < j$ for $j = 2, 4, 5, 6, 7.$ The sum $a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}$ is

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Solution

The correct option is C 9
$\frac{5}{7} = \frac{a_{2}}{2!} + \frac{a_{3}}{3!} + \frac{a_{4}}{4!} + \frac{a_{5}}{5!} + \frac{a_{6}}{6!} + \frac{a_{7}}{7!} \Rightarrow \frac{5}{7} = \frac{1}{2} (a_{2} + \frac{1}{3} (a_{3} + \frac{1}{4} (a_{4} + . . . . . . (\frac{a_{7}}{7})))) \frac{10}{7} = a_{2} + \frac{1}{3} (a_{3} + \frac{1}{4} (a_{4} + . . . . . . (\frac{a_{7}}{7}))) 1 + \frac{3}{7} = a_{2} + \frac{1}{3} (a_{3} + \frac{1}{4} (a_{4} + . . . . . . (\frac{a_{7}}{7})))$

So, as expression is less than $1$

$a_{2} = 1 \frac{3}{7} = \frac{1}{3} (a_{3} + \frac{1}{4} (a_{4} + . . . . . . \frac{1}{5} (a_{5} + . . . . . \frac{a_{7}}{7}))) 1 + \frac{2}{7} = a_{3} + \frac{1}{4} (a_{4} + . . . . . . \frac{1}{5} (a_{5} + \frac{1}{6} (a_{6} + \frac{a_{7}}{7}))) a_{3} = 1$

Similarly

$a_{4} = 1 a_{7} = 2 a_{5} = 0 a_{6} = 4$

So, Sum $a_{7} - 1 + 1 + 1 + 4 + 2 = 9$

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Similar questions

Suppose $a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}$ are integers such that $\frac{5}{7} = \frac{a_{2}}{2!} + \frac{a_{3}}{3!} + \frac{a_{4}}{4!} + \frac{a_{5}}{5!} + \frac{a_{6}}{6!} + \frac{a_{7}}{7!}$ where 0 $\leq$ a< j for j= 2,4,5,6,7.

The sum $a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}$ is

Q. Suppose

a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}

are intagers such that

\frac{5}{7} = \frac{a_{2}}{2!} + \frac{a_{3}}{3!} + \frac{a_{4}}{4!} + \frac{a_{5}}{5!} + \frac{a_{6}}{6!} + \frac{a_{7}}{7!}

where

0 \leq a_{j} < j

for

j = 2, 3, 4, 5, 6, 7

. The sum

a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}

is-

The sum $a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}$ is

Q. For an A.P.,

a_{1}, a_{2}, a_{3}, \dots \dots

, if

a_{3} + a_{5} + a_{8} = 11

and

a_{4} + a_{2} = - 2

, then the value of

a_{1} + a_{6} + a_{7}

Q. Let

a_{1}, a_{2}, a_{3}, \dots

be an A.P. such that

a_{3} + a_{5} + a_{8} = 11

and

a_{4} + a_{2} = - 2

. Then the value of

a_{1} + a_{6} + a_{7}

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Suppose a2,a3,a4,a5,a6,a7 are integers such that57=a22!+a33!+a44+a55!+a66!+a77!where 0≤a<j for j=2,4,5,6,7. The sum a2+a3+a4+a5+a6+a7 is