If Sn= displaystyle∑r=1n (2 r+1/r4+2 r3+r2), then S10 is equal to

Question

If Sn= displaystyle∑r=1n (2 r+1/r4+2 r3+r2), then S10 is equal to (A) 1 (B) (121/120) (C) (120/121) (D) (60/61)

Tardigrade Admin · Accepted Answer

S n = displaystyle∑ r =1 n (2 r +1/ r 2( r +1))= displaystyle∑ r =1 n [(1/ r 2)-(1/( r +1)2)] ∴ S 10=((1/1)-(1/22))+((1/22)-(1/32))+ ldots .+((1/102)-(1/112)) S 10=1-(1/121)=(120/121)

Q. If $S_{n} = r = 1 \sum n \frac{2 r + 1}{r ^{4} + 2 r ^{3} + r ^{2}}$ , then $S_{10}$ is equal to

1

$\frac{121}{120}$

$\frac{120}{121}$

$\frac{60}{61}$

Q. If Sn​=r=1∑n​r4+2r3+r22r+1​, then S10​ is equal to

1

120121​

121120​

6160​

Sn​=r=1∑n​r2(r+1)2r+1​=r=1∑n​[r21​−(r+1)21​] ∴S10​=(11​−221​)+(221​−321​)+….+(1021​−1121​) S10​=1−1211​=121120​

Q. If $S_{n} = r = 1 \sum n \frac{2 r + 1}{r ^{4} + 2 r ^{3} + r ^{2}}$ , then $S_{10}$ is equal to

$\frac{121}{120}$

$\frac{120}{121}$

$\frac{60}{61}$