Find the sum of rational terms in the expression of(√2+3^1/5) ^10
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The sum of rational terms in the expansion of (
2
+3
1/5
)
10
is
Hard
Solution
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Correct option is B)
(r+1)th term in the given expansion is given by
t
r+1
=
10
C
r
2
2
10−r
.3
5
r
, where r=0,1,2,3,...,10
For rational terms
r=a multiple of 5 =0,5,10 ....(1)
10−r=a multiple of 2 =0,2,4,6,8,10 ...(2)
From (1) and (2) possible values of r are :0 and 10
∴ sum of rational terms
=t
1
+t
11
=
10
C
0
(
2
)
10
⎝
⎛
3
5
1
⎠
⎞
0
+
10
C
10
(
2
)
0
⎝
⎛
3
5
1
⎠
⎞
10
=2
5
+3
2
=32+9=41
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